Tootfinder

Learning non-Markovian Dynamical Systems with Signature-based Encoders
Eliott Pradeleix, R\'emy Hosseinkhan-Boucher, Alena Shilova, Onofrio Semeraro, Lionel Mathelin
https://arxiv.org/abs/2509.12022

Learning non-Markovian Dynamical Systems with Signature-based Encoders
Neural ordinary differential equations offer an effective framework for modeling dynamical systems by learning a continuous-time vector field. However, they rely on the Markovian assumption - that future states depend only on the current state - which is often untrue in real-world scenarios where the dynamics may depend on the history of past states. This limitation becomes especially evident in settings involving the continuous control of complex systems with delays and memory effects. To capt…

Nonautonomous Dynamical Systems III: Symbolic and Expansive Systems
Zhuo Chen, Jun Jie Miao
https://arxiv.org/abs/2509.11130 https://arxiv.org/pdf/2509.111…

Nonautonomous Dynamical Systems III: Symbolic and Expansive Systems
A nonautonomous dynamical system $(\boldsymbol{X},\boldsymbol{T})=\{(X_{k},T_{k})\}_{k=0}^{\infty}$ is a sequence of continuous mappings $T_{k}:X_{k} \to X_{k+1}$ along a sequence of compact metric spaces $X_{k}$. In this paper, we study the nonautonomous symbolic systems $(\boldsymbolΣ(\boldsymbol{m}),\boldsymbolσ)$ and nonautonomous expansive dynamical systems. We prove homogeneous properties and provide the formulae for topological pressures $\underline{P},\overline{P},P^{\mathrm{B}},P^{\m…

Next-Generation Reservoir Computing for Dynamical Inference
Rok Cestnik, Erik A. Martens
https://arxiv.org/abs/2509.11338 https://arxiv.org/pdf/2509.11338

Next-Generation Reservoir Computing for Dynamical Inference
We present a simple and scalable implementation of next-generation reservoir computing for modeling dynamical systems from time series data. Our approach uses a pseudorandom nonlinear projection of time-delay embedded input, allowing an arbitrary dimension of the feature space, thus providing a flexible alternative to the polynomial-based projections used in previous next-generation reservoir computing variants. We apply the method to benchmark tasks -- including attractor reconstruction and bi…

High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systems
Nicolas Chatzikiriakos, Kevin Jamieson, Andrea Iannelli
https://arxiv.org/abs/2509.11907

High Effort, Low Gain: Fundamental Limits of Active Learning for Linear Dynamical Systems
In this work, we consider the problem of identifying an unknown linear dynamical system given a finite hypothesis class. In particular, we analyze the effect of the excitation input on the sample complexity of identifying the true system with high probability. To this end, we present sample complexity lower bounds that capture the choice of the selected excitation input. The sample complexity lower bound gives rise to a system theoretic condition to determine the potential benefit of experiment…

Asymmetric radiation in binary systems: Implications for disk evolution and chemistry
Pedro P. Poblete, Nicol\'as Cuello, Antoine Alaguero, Daniel J. Price, Eleonora Bianchi, Christophe Pinte, Fran\c{c}ois Menard
https://arxiv.org/abs/2509.12898

Asymmetric radiation in binary systems: Implications for disk evolution and chemistry
Current models of binary systems often depend on simplified approach of the radiation field, which are unlikely to accurately capture the complexities of asymmetric environments. We investigate the dynamical and chemical implications of a 3D asymmetric radiation field that accounts for the optical properties of sub-structures present in a protoplanetary disk, as well as the inclusion of a secondary radiation source in binary systems. We conducted a series of 3D-SPH hydrodynamical simulations us…

K-Theory and Structural Properties of $C^*$-Algebras Associated with Relative Generalized Boolean Dynamical Systems
Toke Meier Carlsen, Eun Ji Kang
https://arxiv.org/abs/2509.12738

K-Theory and Structural Properties of $C^*$-Algebras Associated with Relative Generalized Boolean Dynamical Systems
We present an explicit formula for the $K$-theory of the $C^*$-algebra associated with a relative generalized Boolean dynamical system $(\CB, \CL, θ, \CI_\af; \CJ)$. In particular, we find concrete generators for the $K_1$-group of $C^*(\CB, \CL, θ, \CI_\af; \CJ)$. We also prove that every gauge-invariant ideal of $C^*(\CB, \CL, θ, \CI_\af; \CJ)$ is Morita equivalent to a $C^*$-algebra of a relative generalized Boolean dynamical system. As a structural application, we show that if the unde…

Selective decoupling in multi-level quantum systems by the SU(2) sign anomaly
Giorgio Anfuso, Giulia Piccitto, Vittorio Romano, Elisabetta Paladino, Giuseppe Falci
https://arxiv.org/abs/2507.12056

Selective decoupling in multi-level quantum systems by the SU(2) sign anomaly
We investigate dynamical decoupling operated by $2π$-pulses in a two-level subspaces of a multilevel system showing that it may leads to selective decoupling. This provides a flexible strategy for decoupling transitions in a quantum network, when control to directly address them is not available which can be use to control internode interaction or actively suppress decoherence

Dynamical Transitions in Trapped Superfluids Excited by Alternating Fields
V. I. Yukalov, E. P. Yukalova
https://arxiv.org/abs/2509.11166 https://arxiv.org…

Dynamical Transitions in Trapped Superfluids Excited by Alternating Fields
The paper presents a survey of some dynamical transitions in nonequilibrium trapped Bose-condensed systems subject to the action of alternating fields. Nonequilibrium states of trapped systems can be realized in two ways, resonant and nonresonant. Under resonant excitation, several coherent modes are generated by external alternating fields, whose frequencies are tuned to resonance with some transition frequencies of the trapped system. A Bose system of trapped atoms with Bose-Einstein condensa…

A Time-Series Foundation Model by Universal Delay Embedding
Zijian Wang, Peng Tao, Jifan Shi, Rui Bao, Rui Liu, Luonan Chen
https://arxiv.org/abs/2509.12080 https://

A Time-Series Foundation Model by Universal Delay Embedding
This study introduces Universal Delay Embedding (UDE), a pretrained foundation model designed to revolutionize time-series forecasting through principled integration of delay embedding representation and Koopman operator prediction. Leveraging Takens' embedding theorem, UDE as a dynamical representation of observed data constructs two-dimensional subspace patches from Hankel matrices, theoretically preserving dynamical and topological properties of underlying dynamical systems. Such patches are…

Emergent order from mixed chaos at low temperature
Pavel Chvykov, Jeremy England
https://arxiv.org/abs/2509.11583 https://arxiv.org/pdf/2509.11583

Emergent order from mixed chaos at low temperature
This paper explores a novel connection between a thermodynamic and a dynamical systems perspective on emergent dynamical order. We provide evidence for a conjecture that Hamiltonian systems with mixed chaos spontaneously find regular behavior when minimally coupled to a thermal bath at sufficiently low temperature. Numerical evidence across a diverse set of five dynamical systems supports this conjecture, and allows us to quantify corollaries about the organization timescales and disruption of …

Uniform Diophantine approximation on the plane for $\beta$-dynamical systems
Xiaohui Fu, Junjie Shi, Chen Tian
https://arxiv.org/abs/2509.10863 https://arx…

Uniform Diophantine approximation on the plane for $β$-dynamical systems
In this paper, we investigate the two-dimensional uniform Diophantine approximation in $β$-dynamical systems. Let $β_i > 1(i=1,2)$ be real numbers, and let $T_{β_i}$ denote the $β_i$-transformation defined on $[0, 1]$. For each $(x, y) \in[0,1]^2$, we define the asymptotic approximation exponent $$ v_{β_1, β_2}(x, y)=\sup \left\{0 \leq v<\infty: \begin{array}{l} T_{β_1}^n x<β_1^{-n v} \\ T_{β_2}^n y<β_2^{-n v} \end{array} \text { for infinitely many } n \in \mathbb{N}\right\} \text {,…

Linear Algebra Problems Solved by Using Damped Dynamical Systems on the Stiefel Manifold
M Gulliksson, A Oleynik, M Ogren, R Bakhshandeh-Chamazkoti
https://arxiv.org/abs/2510.10535

Linear Algebra Problems Solved by Using Damped Dynamical Systems on the Stiefel Manifold
We develop a new method for solving minimization problems on the Stiefel Manifold using damped dynamical systems. The constraints are satisfied in the limit by an additional damped dynamical system. The method is illustrated by numerical experiments and compared to a state-of-the-art conjugate gradient method.

Nambu Non-equilibrium Thermodynamics III: Application to specific phenomena
So Katagiri, Yoshiki Matsuoka, Akio Sugamoto
https://arxiv.org/abs/2509.12641 https://

Nambu Non-equilibrium Thermodynamics III: Application to specific phenomena
We apply Nambu non-equilibrium thermodynamics (NNET)-a dynamics with multiple Hamiltonians coupled to entropy-induced dissipation-to paradigmatic far-from-equilibrium systems. Concretely, we construct NNET realizations for the Belousov-Zhabotinsky (BZ) reaction (oscillatory), the Hindmarsh-Rose neuron model (spiking), and the Lorenz and Chen systems (chaotic), and analyze their dynamical and thermodynamic signatures. Across all cases the velocity field cleanly decomposes into a reversible Nambu…

On $q$-analogs of the $3x 1$ Dynamical System
Kenneth G. Monks
https://arxiv.org/abs/2508.10153 https://arxiv.org/pdf/2508.10153

On $q$-analogs of the $3x+1$ Dynamical System
The $3x+1$ Conjecture asserts that the $T$-orbit of every positive integer $x$ contains $1$, where $T$ maps $x$ to $x/2$ for $x$ even and to $(3x+1)/2$ for $x$ odd. Several authors have studied the analogous map, $T_q$, which maps $x\in F_2[q]$ to $x/q$ if $q$ divides $x$ and $((1+q)x+1)/q$ otherwise. In particular, they showed that the $T_q$-orbit of every polynomial contains $1$. This seems analogous to the $3x+1$ conjecture, but does not prove the conjecture itself, as the dynamical systems …

Partial Dirac Structures and Dynamical Systems
Fernand Pelletier, Patrick Cabau
https://arxiv.org/abs/2508.10799 https://arxiv.org/pdf/2508.10799

Partial Dirac Structures and Dynamical Systems
In a previous paper (PeCa24), the notion of Dirac structure in finite dimension was extended to the convenient setting. In particular, we introduce the notion of \emph{partial Dirac structure on a convenient manifold} and look for which all geometrical results in finite dimension which are still true in this infinite dimensional framework. Note that this context is justified by many mechanical infinite dimensional examples which recover all the classical ones, such as Hilbert, Banach, Fréchet …

A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge
Jibitesh Dutta, Wompherdeiki Khyllep, Saikat Chakraborty, Daniele Gregoris, Khamphee Karwan
https://arxiv.org/abs/2508.09530

A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge
We present a unified dynamical systems framework for spatially flat FLRW cosmology in $f(Q)$ gravity, covering all three connection branches via a single set of Hubble-normalised variables without fixing $f(Q)$ \textit{a priori}. This connection-agnostic, model-independent approach enables direct comparison across branches and reveals generic structural features that are not apparent in model or connection-specific analyses. Beyond fixed points, we identify invariant submanifolds, model-indepen…

Symmetry Groups of Basins of Attraction in Equivariant Dynamical Systems
Xiao Xie
https://arxiv.org/abs/2509.11403 https://arxiv.org/pdf/2509.11403

Symmetry Groups of Basins of Attraction in Equivariant Dynamical Systems
This paper investigates the symmetry properties of basins of attraction and their boundaries in equivariant dynamical systems. While the symmetry groups of compact attractors are well understood, the corresponding analysis for non-compact basins and their boundaries has remained underdeveloped. We establish a rigorous theoretical framework demonstrating the hierarchical inclusion of a chain of symmetry groups, showing that boundary symmetries can strictly exceed those of attractors and their ba…

Dynamic Modeling, Analysis, and Validation of Dual-Port Grid-Forming Control for Hybrid AC/DC Systems
Irina Suboti\'c, Dominic Gro{\ss}, Alexander Winkens, Julian Jansen, Florian Klein-Helmkamp, Andreas Ulbig
https://arxiv.org/abs/2509.11318

Dynamic Modeling, Analysis, and Validation of Dual-Port Grid-Forming Control for Hybrid AC/DC Systems
This work investigates the transient and dynamical behavior of hybrid AC/DC systems using dual-port grid-forming (GFM) control. A generalized modeling framework for hybrid AC/DC networks is first introduced that accounts for converter, control, and network circuit dynamics and arbitrary network topologies. This modeling framework is applied to low-voltage networks to analyze the performance of dual-port grid-forming (GFM) control. The results demonstrate that active damping by dual-port GFM con…

No Giant Planets in the Eta Cassiopeiae System: Dynamical Implications of a Wide Binary Companion
Stephen R. Kane, Zhexing Li, Michelle L. Hill, Skylar D'Angiolillo, Benjamin J. Fulton, Andrew W. Howard
https://arxiv.org/abs/2509.12334

No Giant Planets in the Eta Cassiopeiae System: Dynamical Implications of a Wide Binary Companion
Given the vast number of stars that exist within binary systems, it remains important to explore the effect of binary star environments on the formation and evolution of exoplanetary systems. Nearby binaries provide opportunities to characterize their properties and orbits through a combination of radial velocities, astrometry, and direct imaging. Eta Cassiopeiae is a bright, well-known binary system for which recent observations have provided greatly improved stellar masses and orbital paramet…

Kalman Filtering of Stationary Graph Signals
Yang Chen, Yeonju Lee, Yao Shi, Qiyu Sun
https://arxiv.org/abs/2509.12605 https://arxiv.org/pdf/2509.12605

Kalman Filtering of Stationary Graph Signals
In this paper, we propose a novel definition of stationary graph signals, formulated with respect to a symmetric graph shift, such as the graph Laplacian. We show that stationary graph signals can be generated by transmitting white noise through polynomial graph channels, and that their stationarity is preserved under polynomial channel transmission. In this paper, we also investigate Kalman filtering to dynamical systems characterized by polynomial state and observation matrices. We demonstr…

Global dynamical stability for KMS-states
Heide Narnhofer
https://arxiv.org/abs/2508.10728 https://arxiv.org/pdf/2508.10728

Global dynamical stability for KMS-states
The Hugenholz-Boltzmann-evolution is generalized to strongly interacting systems on the lattice. Under appropriate assumptions states stable under this evolution are shown to satify the KMS-condition. How far these assumptions are reasonable is discussed.

LevelSetPy: A GPU-Accelerated Package for Hyperbolic Hamilton-Jacobi Partial Differential Equations
Lekan Molu
https://arxiv.org/abs/2507.11542 https://

LevelSetPy: A GPU-Accelerated Package for Hyperbolic Hamilton-Jacobi Partial Differential Equations
This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In scope, we provide implementations of numerical algorithms for the resolution of Hamilton-Jacobi-Isaacs equations: the spatial derivatives of the associated value function via upwinding, the Hamiltonian via Lax-Friedrichs schemes, and the integration of the Hamil…

Luminous Fast Blue Optical Transients as "Failed" Gravitational Wave Sources: Helium Core$-$Black Hole Mergers Following Delayed Dynamical Instability
Jakub Klencki, Brian D. Metzger
https://arxiv.org/abs/2510.09745

Luminous Fast Blue Optical Transients as "Failed" Gravitational Wave Sources: Helium Core$-$Black Hole Mergers Following Delayed Dynamical Instability
Binaries in which a massive donor star undergoes an extended ($\gtrsim$ kyr) phase of stable mass transfer onto a black hole (BH) accretor offer a promising channel for creating LIGO gravitational wave sources. However, in many systems the mass transfer terminates prematurely in a dynamical instability at orbital periods of a few days, culminating in the BH plunging into the donor and potentially disrupting and accreting its helium core at highly super-Eddington rates. Combining a suite of bina…

Spontaneous formation of subsystem and bath under accordion-type driving
Suyang Lin, Ming Gong, Congjun Wu
https://arxiv.org/abs/2509.12761 https://arxiv.o…

Spontaneous formation of subsystem and bath under accordion-type driving
Floquet modulations often yield effective Hamiltonians not easily accessible in traditional time-dependent systems, which brings opportunities for exploring novel physics of quantum dynamics. We investigate a Floquet system exhibiting translational symmetry at any fixed time but the spatial periodicity is time-dependent. Such a system is a natural platform for studying thermalization and novel dynamical structures. We find that the single-particle Hilbert space spontaneously develops a structur…

Entering the Wind Roche Lobe Overflow realm in Symbiotic Systems
R. F. Maldonado, J. A. Toal\'a, E. Tejeda, J. B. Rodr\'iguez-Gonz\'alez
https://arxiv.org/abs/2508.06727

Entering the Wind Roche Lobe Overflow realm in Symbiotic Systems
We present a suite of dynamical simulations designed to explore the orbital and accretion properties of compact (2--7 AU) symbiotic systems, focusing on wind accretion, drag forces, and tidal interactions. Using three levels of physical complexity, we model systems of accreting white dwarfs (WDs) with masses of 0.7, 1.0, and 1.2 M$_\odot$ orbiting evolving Solar-like stars with 1, 2, and 3 M$_\odot$. We show that systems alternate between standard wind accretion and Wind Roche Lobe Overflow (WR…

Dynamical systems as enriched functors
Suddhasattwa Das, Tomoharu Suda
https://arxiv.org/abs/2509.05900 https://arxiv.org/pdf/2509.05900

Dynamical systems as enriched functors
This article presents a general description of dynamical systems using the language of enriched functors and enriched natural transformations. This framework is essential to establish the equivalence of three descriptions of dynamics -- a semigroup action on the domain; a parameterized family of endomorphisms; and a transformation of time-space into the collection of endomorphisms. A collection of categorical axioms are presented that provides a complete categorical language to develop dynamica…

Fractional-Order Nesterov Dynamics for Convex Optimization
Tumelo Ranoto
https://arxiv.org/abs/2509.11987 https://arxiv.org/pdf/2509.11987

Fractional-Order Nesterov Dynamics for Convex Optimization
We propose and analyze a class of second-order dynamical systems for continuous-time optimization that incorporate fractional-order gradient terms. The system is given by \begin{equation} \ddot{x}(t) + \fracα{t}\dot{x}(t) + \nabla^θ f(x(t)) = 0, \end{equation} where $θ\in (1,2)$, and the fractional operators are interpreted in the sense of Caputo, Riemann--Liouville, and Grünwald--Letnikov derivatives. This formulation interpolates between memory effects of fractional dynamics and higher-or…

Fundamental limitations of sensitivity metrics for anomaly impact analysis in LTI systems
Jingwei Dong, Kangkang Zhang, Anh Tung Nguyen, Andr\'e M. H. Teixeira
https://arxiv.org/abs/2509.11194

Fundamental limitations of sensitivity metrics for anomaly impact analysis in LTI systems
This study establishes a connection between the output-to-output gain (OOG), a sensitivity metric quantifying the impact of stealthy attacks, and a novel input-to-input gain (IIG) introduced to evaluate fault sensitivity under disturbances, and investigates their fundamental performance limitations arising from the transmission zeros of the underlying dynamical system. Inspired by the OOG, which characterizes the maximum performance loss caused by stealthy attacks, the IIG is proposed as a new …

Survival and Detection of Symmetry-Protected Topology in Loop Quenches
Nicol\`o Forcellini, Mikl\'os Horv\'ath, Panagiotis Kotetes
https://arxiv.org/abs/2508.09270 https…

Survival and Detection of Symmetry-Protected Topology in Loop Quenches
We explore a class of dynamical protocols - that we term loop quenches - which are tailored for the study of symmetry-protected topological (SPT) systems. In loop quenches, SPT phases can survive even out of equilibrium, thus evading the dynamical violation of their protecting symmetry. Moreover, we demonstrate that employing loop quenches allows to detect the equilibrium topology via measurable dynamical quantities. Focusing on chiral-SPT phases, we introduce the Loschmidt chirality amplitude …

The Fundamental Theorem of Dynamical Systems: all at once and all in the same place
Andrew D. Lewis
https://arxiv.org/abs/2508.10525 https://arxiv.org/pdf/…

The Fundamental Theorem of Dynamical Systems: all at once and all in the same place
The so-called Fundamental Theorem of Dynamical Systems -- which(1) relates attractors and repellers to the chain recurrent set and (2) gives the existence of a complete Lyapunov function -- can be seen as a means of separating out ``recurrent'' and ``transient'' dynamics. An overview of this theorem is given in its various guises, continuous-time/discrete-time and flows/semiflows. As part of this overview, a unified approach is developed for working simultaneously with both the continuous-time …

A shortcut through the macroscopic fluctuation theory: a generalised Fick law
Th\'eotim Berlioz, Olivier B\'enichou, Aur\'elien Grabsch
https://arxiv.org/abs/2509.12017

A shortcut through the macroscopic fluctuation theory: a generalised Fick law
The macroscopic fluctuation theory is a powerful tool to characterise the large scale dynamical properties of diffusive systems, both in- and out-of-equilibrium. It relies on an action formalism in which, at large scales, the dynamics is fully determined by the minimum of the action. Within this formalism, the analysis of the statistical properties of a given observable reduces to solving the Euler-Lagrange equations with the appropriate boundary conditions. One must then compute the action at …

MODE: Learning compositional representations of complex systems with Mixtures Of Dynamical Experts
Nathan Quiblier, Roy Friedman, Matthew Ricci
https://arxiv.org/abs/2510.09594 …

MODE: Learning compositional representations of complex systems with Mixtures Of Dynamical Experts
Dynamical systems in the life sciences are often composed of complex mixtures of overlapping behavioral regimes. Cellular subpopulations may shift from cycling to equilibrium dynamics or branch towards different developmental fates. The transitions between these regimes can appear noisy and irregular, posing a serious challenge to traditional, flow-based modeling techniques which assume locally smooth dynamics. To address this challenge, we propose MODE (Mixture Of Dynamical Experts), a graphic…

Crosslisted article(s) found for astro-ph.CO. https://arxiv.org/list/astro-ph.CO/new
[1/1]:
- Extending the Dynamical Systems Toolkit: Coupled Fields in Multiscalar Dark Energy
Daniele Licciardello, Saba Rahimy, Ivonne Zavala

Escape-Induced Temporally Correlated Noise Driven Universality Crossover
Mrinal Manna, Sourav Mukherjee, Soumen Giri, Pramod Bhakuni, Sajal Barman, Arnab Kumar Pariari, Anil Gome, Markus Hucker, V. Raghavendra Reddy, Anupam Roy, Sudipta Roy Barman, Smarajit Karmakar, Chandana Mondal, Rajib Batabyal
https://arxiv.org/abs/2510.12593

Escape-Induced Temporally Correlated Noise Driven Universality Crossover
Universal behavior in far-from-equilibrium systems is driven by interactions between transport processes and noise structure. The Kardar-Parisi-Zhang (KPZ) framework predicts that extensions incorporating conserved currents or temporally correlated noise give rise to distinct growth morphologies and universality classes, yet direct experimental realization has remained elusive. Here, we report atomically resolved Sn thin-film growth on Sb-doped MnBi$_2$Te$_4$, revealing a sharp dynamical crosso…

@…

Dynamic mode decomposition for detecting transient activity via sparsity and smoothness regularization
Yutaro Tanaka, Hiroya Nakao
https://arxiv.org/abs/2508.10266 https://

Dynamic mode decomposition for detecting transient activity via sparsity and smoothness regularization
Dynamic Mode Decomposition (DMD) is a data-driven modal decomposition technique that extracts coherent spatio-temporal structures from high-dimensional time-series data. By decomposing the dynamics into a set of modes, each associated with a single frequency and a growth rate, DMD enables a natural modal decomposition and dimensionality reduction of complex dynamical systems. However, when DMD is applied to transient dynamics, even if a large number of modes are used, it remains difficult to in…

Train Stochastic Non Linear Coupled ODEs to Classify and Generate
Stefano Gagliani, Feliciano Giuseppe Pacifico, Lorenzo Chicchi, Duccio Fanelli, Diego Febbe, Lorenzo Buffoni, Raffaele Marino
https://arxiv.org/abs/2510.12286

Train Stochastic Non Linear Coupled ODEs to Classify and Generate
A general class of dynamical systems which can be trained to operate in classification and generation modes are introduced. A procedure is proposed to plant asymptotic stationary attractors of the deterministic model. Optimizing the dynamical system amounts to shaping the architecture of inter-nodes connection to steer the evolution towards the assigned equilibrium, as a function of the class to which the item - supplied as an initial condition - belongs to. Under the stochastic perspective, po…

Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields
Wayne Peng, Yen-Ju Chen
https://arxiv.org/abs/2508.08621 https://arxiv.org/pdf/25…

Periodicity and Dynamical Systems of Dickson Polynomials in Finite Fields
This paper investigates the dynamical properties of Dickson polynomials over finite fields, focusing on the periodicity and structural behavior of their iterated sequences. We introduce and analyze the sequence \( [D_n(x, α) \mod (x^q - x)]_n \), where \( D_n(x, α) \) denotes a Dickson polynomial of the first kind, and explore its periodic nature when reduced modulo \( x^q - x \). We derive explicit formulas for the period of these sequences, particularly in the case when \( n \) is coprime t…

Dilations of non-Markovian dynamical systems on graphs
Raj Dahya
https://arxiv.org/abs/2508.07511 https://arxiv.org/pdf/2508.07511

Dilations of non-Markovian dynamical systems on graphs
To generalise evolutions families we consider systems of contractions $\{φ(u, v)\}_{(u, v) \in E}$ defined on the edges of a graph $\mathcal{G} = (Ω, E)$. In this setup the Markov property, or \emph{divisibility}, can be modelled via $φ(u, v)φ(v, w) = φ(u, w)$ for edges $(u, v), (v, w), (u, w) \in E$. We obtain results in three settings: 1) contractive Banach space operators; 2) positive unital maps on $C^{\ast}$-algebras}; and 3) CPTP-maps on trace class operators on a Hilbert space. In t…

Zeroes of Eigenfunctions of Schr\"odinger Operators after Schwartzman
Willie Wai-Yeung Wong
https://arxiv.org/abs/2509.09739 https://arxiv.org/pdf/250…

Zeroes of Eigenfunctions of Schrödinger Operators after Schwartzman
Consider a complete, connected, smooth, oriented Riemannian manifold $(M,g)$ with boundary, such that the first Betti number vanishes. Sol Schwartzman proved that for Schrödinger operators of the form $-Δ_g + V$ where $\Im(V)$ is signed, if $f: M\to\mathbb{C}$ is a non-vanishing element of its kernel, then $f$ has constant phase. The proof relied on dynamical systems methods applied to the gradient flow of the phase of $f$. In this manuscript we provide a more direct PDE argument that proves …

An Algebraic Proof of the Polynomial Version of van der Waerden's Theorem
Javad Jafari, Mohammad Akbari Tootkaboni
https://arxiv.org/abs/2508.06090 https://

An Algebraic Proof of the Polynomial Version of van der Waerden's Theorem
The polynomial version of van der Waerden's theorem, proved using dynamical systems by V. Bergelson and A. Leibman in 1996, \cite{Bergelson1996}, significantly highlighted the role of dynamical systems in addressing problems related to monochromatic configurations within algebraic structures. In this paper, by introducing symbolic polynomials, we aim to provide an alternative proof of the polynomial version of van der Waerden's theorem relying solely on Stone-Čech compactification of an infini…

Lyapunov stability of the Euler method
C\'edric Josz
https://arxiv.org/abs/2509.11415 https://arxiv.org/pdf/2509.11415…

Lyapunov stability of the Euler method
We extend the Lyapunov stability criterion to Euler discretizations of set-valued dynamical systems. It relies on a pair of Lyapunov functions, one in continuous time and one in discrete time.

Periodic orbits underlying spatiotemporal chaos in the Lugiato-Lefever model
Andrey Gelash, Savyaraj Deshmukh, Andrey Shusharin, Tobias M. Schneider, Tobias J. Kippenberg
https://arxiv.org/abs/2509.10283

Periodic orbits underlying spatiotemporal chaos in the Lugiato-Lefever model
We obtain and investigate theoretically a broad family of stable and unstable time-periodic orbits-oscillating Turing rolls (OTR)-in the Lugiato-Lefever model of optical cavities. Using the dynamical systems tools developed in fluid dynamics, we access the OTR solution branches in parameter space and elucidate their bifurcation structure. By tracking these exact invariant solutions deeply into the chaotic region of the modulation instability, we connect the main dynamical regimes of the Lugiato…

Data-driven discovery of dynamical models in biology
Bartosz Prokop, Lendert Gelens
https://arxiv.org/abs/2509.06735 https://arxiv.org/pdf/2509.06735

Data-driven discovery of dynamical models in biology
Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales. Classical modeling derives explicit governing equations, often systems of differential equations, by combining mechanistic assumptions, experimental observations, and known physical laws. The growing complexity of biological processes has, however, motivated…

Extreme Event Precursor Prediction in Turbulent Dynamical Systems via CNN-Augmented Recurrence Analysis
Rahul Agarwal, Mustafa A. Mohamad
https://arxiv.org/abs/2508.04301 https:…

Extreme Event Precursor Prediction in Turbulent Dynamical Systems via CNN-Augmented Recurrence Analysis
We present a general framework to predict precursors to extreme events in turbulent dynamical systems. The approach combines phase-space reconstruction techniques with recurrence matrices and convolutional neural networks to identify precursors to extreme events. We evaluate the framework across three distinct testbed systems: a triad turbulent interaction model, a prototype stochastic anisotropic turbulent flow, and the Kolmogorov flow. This method offers three key advantages: (1) a threshold-…

Bounds of Validity for Bifurcations of Equilibria in a Class of Networked Dynamical Systems
Pranav Gupta, Ravi Banavar, Anastasia Bizyaeva
https://arxiv.org/abs/2510.10215 https…

Bounds of Validity for Bifurcations of Equilibria in a Class of Networked Dynamical Systems
Local bifurcation analysis plays a central role in understanding qualitative transitions in networked nonlinear dynamical systems, including dynamic neural network and opinion dynamics models. In this article we establish explicit bounds of validity for the classification of bifurcation diagrams in two classes of continuous-time networked dynamical systems, analogous in structure to the Hopfield and the Firing Rate dynamic neural network models. Our approach leverages recent advances in computi…

Spin and Obliquity Distributions of Low-mass Planets Shaped by Dynamical Instability
Dieran Wang (TDLI), Jiaru Li (CIERA), Dong Lai (TDLI, Cornell)
https://arxiv.org/abs/2510.11785

Spin and Obliquity Distributions of Low-mass Planets Shaped by Dynamical Instability
Exoplanetary systems hosting multiple low-mass planets are thought to have experienced dynamical instability, during which planet-planet collisions and mergers occur; these collisions can impart substantial amount of angular momentum to the merger remnants, changing the obliquities of the resulting planets significantly. In this work, we carry out a series of $N$-body experiments to investigate the spin magnitude $(|\vec{S}|)$ and obliquity $(θ_{\rm SL})$ distributions of low-mass ex…

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Towards sharp regularity: Full-dimensional tori in $ C^\infty $ vector fields over $ \mathbb{T}^\...
Zhicheng Tong, Yong Li

Towards Foundation Inference Models that Learn ODEs In-Context
Maximilian Mauel, Manuel Hinz, Patrick Seifner, David Berghaus, Ramses J. Sanchez
https://arxiv.org/abs/2510.12650

Towards Foundation Inference Models that Learn ODEs In-Context
Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging, especially if the data is sparse or noisy. We introduce FIM-ODE (Foundation Inference Model for ODEs), a pretrained neural model designed to estimate ODEs zero-shot (i.e., in context) from sparse and noisy observations. Trained on synthetic data, the model utilizes a …

Two-point Random Gradient-free Methods for Model-free Feedback Optimization
Amir Mehrnoosh, Gianluca Bianchin
https://arxiv.org/abs/2509.11666 https://arxi…

Two-point Random Gradient-free Methods for Model-free Feedback Optimization
Feedback optimization has emerged as a promising approach for optimizing the steady-state operation of dynamical systems while requiring minimal modeling efforts. Unfortunately, most existing feedback optimization methods rely on knowledge of the plant dynamics, which may be difficult to obtain or estimate in practice. In this paper, we introduce a novel randomized two-point gradient-free feedback optimization method, inspired by zeroth-order optimization techniques. Our method relies on functi…

Crosslisted article(s) found for nlin.AO. https://arxiv.org/list/nlin.AO/new
[1/1]:
- Dynamical symmetry breaking described by cubic nonlinear Klein-Gordon equations
Yasuhiro Takei, Yoritaka Iwata

Pulsations in Binary Star Systems
John Southworth, Dominic Bowman
https://arxiv.org/abs/2509.08426 https://arxiv.org/pdf/2509.08426

Pulsations in Binary Star Systems
High-precision and long-duration light curves from space telescopes have revolutionized the fields of asteroseismology and binary star systems. In particular, the number of pulsating systems in eclipsing binaries has drastically increased thanks to space-based observations covering almost the entire sky. When combined with multi-epoch spectroscopy, this allows us not only to measure model-independent dynamical masses and radii for thousands of eclipsing binary systems, but also facilitates the …

Phase space analysis of an exponential model in $f(Q)$ gravity including linear dark-sector interactions
Ivan R. Vasquez, A. Oliveros
https://arxiv.org/abs/2510.12020 https://…

Phase space analysis of an exponential model in $f(Q)$ gravity including linear dark-sector interactions
We present a cosmological analysis of an exponential $f(Q)$ gravity model, within the dynamical systems formalism. Following the method introduced by Böhmer \textit{et al} [Universe \textbf{9} no.4, 166 (2023)], the modified Friedmann modified equations are successfully reduced to an autonomous system. Given the exponential form of $f(Q)$, the equilibrium conditions result in transcendental equations, which we approximate to identify the critical points. We therefore perform a general stabilit…

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Choice Paralysis in Evolutionary Games
Brendon G. Anderson
https://…

Moment closure through spectral expansion in open stochastic systems
Gianni Valerio Vinci, Roberto Benzi, Maurizio Mattia
https://arxiv.org/abs/2508.10654 https://

Moment closure through spectral expansion in open stochastic systems
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general spectral expansion, which clarifies the connection between the relaxation dynamics of arbitrary moments and the intrinsic time scales of the system. Within this framework, we address the moment-closure problem in a way that streamline the conventional treatm…

Large scale dynamical response of interacting $1d$ Fermi systems
Marcello Porta, Giuseppe Scola, Harman Preet Singh
https://arxiv.org/abs/2509.08665 https://

Large scale dynamical response of interacting $1d$ Fermi systems
We consider the dynamics of a class of weakly interacting, gapless $1d$ fermionic systems, in presence of small external perturbations slowly varying in space and in time. We consider the evolution of the expectation values of the charge density and of the current density, in the thermodynamic limit and for low enough temperatures. We prove the validity and the asymptotic exactness of linear response in the limit of vanishing space-time variation of the perturbation, and we provide the explicit…

Universally Robust Control of Open Quantum Systems
Lixiang Ding, Jingtao Fan, Xingze Qiu
https://arxiv.org/abs/2508.07379 https://arxiv.org/pdf/2508.07379

Universally Robust Control of Open Quantum Systems
Mitigating noise-induced decoherence is the central challenge in controlling open quantum systems. While existing robust protocols often require precise noise models, we introduce a universal framework for noise-agnostic quantum control that achieves high-fidelity operations without prior environmental noise characterization. This framework capitalizes on the dynamical modification of the system-environment coupling through control drives, an effect rigorously encoded in the dynamical equation.…

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Density of thin film billiard reflection pseudogroup in Hamiltonian symplectomorphism pseudogroup
Alexey Glutsyuk

Hybrid State Estimation of Uncertain Nonlinear Dynamics Using Neural Processes
Devin Hunter, Chinwendu Enyioha
https://arxiv.org/abs/2509.12522 https://arx…

Hybrid State Estimation of Uncertain Nonlinear Dynamics Using Neural Processes
Various neural network architectures are used in many of the state-of-the-art approaches for real-time nonlinear state estimation in dynamical systems. With the ever-increasing incorporation of these data-driven models into the estimation domain, models with reliable margins of error are required -- especially for safety-critical applications. This paper discusses a novel hybrid, data-driven state estimation approach based on the physics-informed attentive neural process (PI-AttNP), a model-inf…

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Heavy repulsion of clusters in Bernoulli percolation
Sasha Bell, Tasmin Chu, Owen Rodgers, Grigory Terlov, Anush Tserunyan

Prethermal gauge structure and surface growth in $\mathbb{Z}_2$ lattice gauge theories
Lukas Homeier, Andrea Pizzi, Hongzheng Zhao, Jad C. Halimeh, Fabian Grusdt, Ana Maria Rey
https://arxiv.org/abs/2510.12800

Prethermal gauge structure and surface growth in $\mathbb{Z}_2$ lattice gauge theories
Universal aspects of thermalization in interacting many-body systems are typically challenging to derive microscopically, yet provide a powerful framework for understanding emergent phenomena. Here, we numerically study the mean-field dynamics of a $(2+1)$D spin system with thousands of spins and show that experimentally-feasible two-body Ising interactions can stabilize a prethermal $\mathbb{Z}_2$ lattice gauge structure with dynamical matter, manifested by a gauge-invariant plateau with expon…

Automatic Regression for Governing Equations with Control (ARGOSc)
Amir Bahador Javadi, Amin Kargarian, Mort Naraghi-Pour
https://arxiv.org/abs/2509.09784 https://

Automatic Regression for Governing Equations with Control (ARGOSc)
Learning the governing equations of dynamical systems from data has drawn significant attention across diverse fields, including physics, engineering, robotics and control, economics, climate science, and healthcare. Sparse regression techniques, exemplified by the Automatic Regression for Governing Equations (ARGOS) framework, have demonstrated effectiveness in extracting parsimonious models from time series data. However, real-world dynamical systems are driven by input control, external forc…

(Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
C. Sard\'on, X. Zhao
https://arxiv.org/abs/2510.08307 https://arxiv.org/pdf/2510.0830…

(Quasi) Hamiltonian Systems and Non-Decomposable Poisson Geometry
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of nondecomposable generalized Poisson brackets and the dynamical behavior of systems exhibiting specific symmetry properties. In particular, we demonstrate that if a dynamical system admits suitable invariance conditions -- such as those arising from Lie symmetries or conser…

On Sets of Periodic Orbit Lengths in Finitely Presented Dynamical Systems
Huub de Jong
https://arxiv.org/abs/2510.10848 https://arxiv.org/pdf/2510.10848

On Sets of Periodic Orbit Lengths in Finitely Presented Dynamical Systems
We classify the sets of natural numbers $n$ for which certain dynamical systems $(X,f)$ on a compact metric space $X$ have a periodic point of (least) period $n$. Interest in this question dates back to Sharkovskii's theorem for continuous maps on intervals of the real line, but it also ties to checkable conditions for Krieger's embedding theorem for symbolic dynamical systems. Given a system for which the logarithmic derivative of the Artin-Mazur zeta function is rational, we use the Skolem-Ma…

Task-Level Insights from Eigenvalues across Sequence Models
Rahel Rickenbach, Jelena Trisovic, Alexandre Didier, Jerome Sieber, Melanie N. Zeilinger
https://arxiv.org/abs/2510.09379

Task-Level Insights from Eigenvalues across Sequence Models
Although softmax attention drives state-of-the-art performance for sequence models, its quadratic complexity limits scalability, motivating linear alternatives such as state space models (SSMs). While these alternatives improve efficiency, their fundamental differences in information processing remain poorly understood. In this work, we leverage the recently proposed dynamical systems framework to represent softmax, norm and linear attention as dynamical systems, enabling a structured compariso…

Safety Critical Model Predictive Control Using Discrete-Time Control Density Functions
Sriram S. K. S. Narayanan, Sajad Ahmadi, Javad Mohammadpour Velni, Umesh Vaidya
https://arxiv.org/abs/2509.13257

Safety Critical Model Predictive Control Using Discrete-Time Control Density Functions
This paper presents MPC-CDF, a new approach integrating control density functions (CDFs) within a model predictive control (MPC) framework to ensure safety-critical control in nonlinear dynamical systems. By using the dual formulation of the navigation problem, we incorporate CDFs into the MPC framework, ensuring both convergence and safety in a discrete-time setting. These density functions are endowed with a physical interpretation, where the associated measure signifies the occupancy of syst…

Universal Analog Computation: Fra\"iss\'e limits of dynamical systems
Levin Hornischer
https://arxiv.org/abs/2510.10184 https://arxiv.org/pdf/2510…

Universal Analog Computation: Fraïssé limits of dynamical systems
Analog computation is an alternative to digital computation, that has recently re-gained prominence, since it includes neural networks. Further important examples are cellular automata and differential analyzers. While analog computers offer many advantages, they lack a notion of universality akin to universal digital computers. Since analog computers are best formalized as dynamical systems, we review scattered results on universal dynamical systems, identifying four senses of universality and…

Speeding up Pontus-Mpemba effects via dynamical phase transitions
Andrea Nava, Reinhold Egger, Bidyut Dey, Domenico Giuliano
https://arxiv.org/abs/2509.09366 https://

Speeding up Pontus-Mpemba effects via dynamical phase transitions
We demonstrate that open quantum systems exhibiting dynamical phase transitions (DPTs) allow for highly efficient protocols implementing the Pontus-Mpemba effect. The relaxation speed-up toward a predesignated target state is tied to the existence of a long metastable time window preceding the DPT and can be exploited in applications to systematically optimize quantum protocols. As paradigmatic example for the connection between DPTs and quantum Mpemba effects, we study one-dimensional (1D) int…

On The Orbital Evolution of Multiple Wide Super-Jupiters: How Disk Migration and Dispersal Shape the Stability of The PDS 70 System
Clarissa R. Do \'O, Jaehan Bae, Quinn M. Konopacky, Jayke S. Nguyen, Patrick Diamond, Krzysztof Go\'zdziewski, Dawid Jankowski
https://arxiv.org/abs/2510.11021…

On The Orbital Evolution of Multiple Wide Super-Jupiters: How Disk Migration and Dispersal Shape the Stability of The PDS 70 System
Direct imaging has revealed exoplanet systems hosting multiple wide-orbit Super-Jupiters, where planet-planet interactions can shape their long-term dynamical evolution. These strong perturbations may lead to orbital instability, raising questions about the long-term survival of such systems. Shortly after formation, planet-disk interactions can shepherd planets into mean-motion resonances, which may promote long-term stability as seen in HR 8799. However, early-stage processes such as disk pho…

Jamming of active particles in narrow pores: Implications for ratchet effect and diffusion coefficient
\v{S}imon Pajger, Franti\v{s}ek Slanina
https://arxiv.org/abs/2508.10483 h…

Jamming of active particles in narrow pores: Implications for ratchet effect and diffusion coefficient
We study the behavior of colloidal active particles interacting via steric repulsion in various quasi-1D geometries. We mainly focus on active particles with high Péclet number. We discuss 3 phenomena closely tied to those systems: motility-induced phase separation (or dynamical freezing), ratchet effect (which takes place if the geometry has broken spatial symmetry), and the enhanced diffusion coefficient. We study those particles using numerical simulations employing an ASEP-like model. Besi…

Sensitivity-Driven Adaptive Surrogate Modeling for Simulation and Optimization of Dynamical Systems
Jonathan R. Cangelosi, Matthias Heinkenschloss
https://arxiv.org/abs/2509.04651

Sensitivity-Driven Adaptive Surrogate Modeling for Simulation and Optimization of Dynamical Systems
This paper develops a surrogate model refinement approach for the simulation of dynamical systems and the solution of optimization problems governed by dynamical systems in which surrogates replace expensive-to-compute state- and control-dependent component functions in the dynamics or objective function. For example, trajectory simulation and optimization tasks for an aircraft depend on aerodynamic coefficient functions whose evaluation requires expensive computational fluid dynamics simulatio…

[2025-09-17 Wed (UTC), 6 new articles found for math.DS Dynamical Systems]
toXiv_bot_toot

Learning Mixtures of Linear Dynamical Systems (MoLDS) via Hybrid Tensor-EM Method
Lulu Gong, Shreya Saxena
https://arxiv.org/abs/2510.06091 https://arxiv.o…

Learning Mixtures of Linear Dynamical Systems (MoLDS) via Hybrid Tensor-EM Method
Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its effectiveness for neural data analysis. Tensor-based moment methods can provide global identifiability guarantees for MoLDS, but their performance degrades under noise and complexity. Commonly used expectation-maximization (EM) methods offer flexibility in fitting…

[2025-09-16 Tue (UTC), 11 new articles found for math.DS Dynamical Systems]
toXiv_bot_toot

Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees
P Sangeerth, David Smith Sundarsingh, Bhabani Shankar Dey, Pushpak Jagtap
https://arxiv.org/abs/2510.10450

Controller for Incremental Input-to-State Practical Stabilization of Partially Unknown systems with Invariance Guarantees
Incremental stability is a property of dynamical systems that ensures the convergence of trajectories with respect to each other rather than a fixed equilibrium point or a fixed trajectory. In this paper, we introduce a related stability notion called incremental input-to-state practical stability (δ-ISpS), ensuring safety guarantees. We also present a feedback linearization based control design scheme that renders a partially unknown system incrementally input-to-state practically stable and …

Computing stabilizing feedback gains for stochastic linear systems via policy iteration method
Xinpei Zhang, Guangyan Jia
https://arxiv.org/abs/2508.05214 https://

Computing stabilizing feedback gains for stochastic linear systems via policy iteration method
In recent years, stabilizing unknown dynamical systems has became a critical problem in control systems engineering. Addressing this for linear time-invariant (LTI) systems is an essential fist step towards solving similar problems for more complex systems. In this paper, we develop a model-free reinforcement learning algorithm to compute stabilizing feedback gains for stochastic LTI systems with unknown system matrices. This algorithm proceeds by solving a series of discounted stochastic linea…

Doubling bifurcations of invariant closed curves in 3D maps
Sayanho Biswas, Soumitro Banerjee, Viktor Avrutin, Iryna Sushko
https://arxiv.org/abs/2509.12943 https://

Doubling bifurcations of invariant closed curves in 3D maps
Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the length of the original ICC. Various methods have been proposed to analyze such bifurcations. We show that the methods proposed so far are not always adequate for analyzing and predicting these bifurcations. We propose a new method to overcome the difficulties.

A quantum computing approach to efficiently simulating correlated materials using impurity models and dynamical mean field theory
Norman Hogan, Efekan K\"okc\"u, Thomas Steckmann, Liam P. Doak, Carlos Mejuto-Zaera, Daan Camps, Roel Van Beeumen, Wibe A. de Jong, A. F. Kemper
https://arxiv.org/abs/2508.05738

A quantum computing approach to efficiently simulating correlated materials using impurity models and dynamical mean field theory
The accurate theoretical description of materials with strongly correlated electrons is a formidable challenge, at the forefront of condensed matter physics and computational chemistry alike, and it is one of the targets for quantum computing. Dynamical Mean Field Theory (DMFT) is a successful approach that predicts behaviors of such systems by incorporating some correlated behavior, but it is limited by the need to calculate the Green's function for the impurity model. This work proposes a fra…

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Irreducibility and periodicity in $\mathbb{Z}^{2}$ symbolic systems
Michael Hochman

Replaced article(s) found for eess.SY. https://arxiv.org/list/eess.SY/new
[1/1]:
- SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data, with App...
Mohammad Amin Basiri, Sina Khanmohammadi

Data-driven approximation of transfer operators for mean-field stochastic differential equations
Eirini Ioannou, Stefan Klus, Gon\c{c}alo dos Reis
https://arxiv.org/abs/2509.09891

Data-driven approximation of transfer operators for mean-field stochastic differential equations
Mean-field stochastic differential equations, also called McKean--Vlasov equations, are the limiting equations of interacting particle systems with fully symmetric interaction potential. Such systems play an important role in a variety of fields ranging from biology and physics to sociology and economics. Global information about the behavior of complex dynamical systems can be obtained by analyzing the eigenvalues and eigenfunctions of associated transfer operators such as the Perron--Frobeniu…

Distance Between Stochastic Linear Systems
Venkatraman Renganathan, Sei Zhen Khong
https://arxiv.org/abs/2509.04014 https://arxiv.org/pdf/2509.04014…

Distance Between Stochastic Linear Systems
This manuscript proposes a distance measure between stochastic linear dynamical systems. While the existing stochastic control theory is well equipped to handle dynamical systems with stochastic uncertainties, a paradigm shift using distance measure based decision making is required for the effective further exploration of the field. As a first step, a distance measure between two linear time invariant stochastic dynamical systems is proposed here, extending the existing distance metrics betwee…

An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications
Xiang Lv
https://arxiv.org/abs/2508.08497 h…

An abstract criterion on the existence and global stability of stationary solutions for random dynamical systems and its applications
We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show that the $ω$-limit sets of all pullback trajectories of semilnear/nonlinear stochastic differential equations (SDEs) with additive/multiplicative white noise are composed of nontrivial random equilibria. The proof is different from the classical RDS scheme, which was established in \cite{CKS}. Furthermore, in the app…

Parameter Robustness in Data-Driven Estimation of Dynamical Systems
Ayush Pandey
https://arxiv.org/abs/2509.06534 https://arxiv.org/pdf/2509.06534

Parameter Robustness in Data-Driven Estimation of Dynamical Systems
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main contribution of this paper is the development of a novel robustness metric for estimation of parametrized linear dynamical systems with and without control actions. For the computation of this metric, we delineate the uncertainty contributions arising from cont…

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Measure-Theoretically Mixing Subshifts of Minimal Word Complexity
Darren Creutz

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Frequency conditions for the global stability of nonlinear delay equations with several equilibria
Mikhail Anikushin, Andrey Romanov

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Advanced creep modelling for polymers: A variable-order fractional calculus approach
Jos\'e Geraldo Telles Ribeiro, Americo Cunha Jr

Koopman Control Factorization: Data-Driven Convex Controller Design for a Class of Nonlinear Systems
Taha Ondogan, Ran Jing, Andrew P. Sabelhaus, Roberto Tron
https://arxiv.org/abs/2510.05359

Koopman Control Factorization: Data-Driven Convex Controller Design for a Class of Nonlinear Systems
Although Koopman operators provide a global linearization for autonomous dynamical systems, nonautonomous systems are not globally linear in the inputs. State (or output) feedback controller design therefore remains nonconvex in typical formulations, even with approximations via bilinear control-affine terms. We address this gap by introducing the Koopman Control Factorization, a novel parameterization of control-affine dynamical systems combined with a feedback controller defined as a linear c…

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Mirrors of conformal dynamics: Interplay between anti-rational maps, reflection groups, Schwarz r...
Mikhail Lyubich, Sabyasachi Mukherjee

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Sharp bounds for the valence of certain logharmonic polynomials
Kirill Lazebnik, Erik Lundberg

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Index theory for non-compact quantum graphs
Daniele Garrisi, Alessandro Portaluri, Li Wu

Fibration Symmetries and Cluster Synchronization in Multi-Body Systems
Margherita Bert\`e, Tommaso Gili
https://arxiv.org/abs/2510.11207 https://arxiv.org/…

Fibration Symmetries and Cluster Synchronization in Multi-Body Systems
Based on recent advances in fibration symmetry theory, we investigate how structural symmetries influence synchronization in systems with higher-order interactions (HOI). Using bipartite graph representations, we identify a node partition in fibres, based on equivalent incidence relations in hypergraphs. We study how identical nodes with an isomorphic input set can synchronize due to structural properties under our specific model assumptions, examining the dynamical model of Kuramoto with highe…

[2025-10-15 Wed (UTC), 8 new articles found for math.DS Dynamical Systems]
toXiv_bot_toot

On the cohomology of homshifts
Nishant Chandgotia, Silv\`ere Gangloff, Benjamin Hellouin de Menibus, Piotr Oprocha
https://arxiv.org/abs/2510.11969 https://

On the cohomology of homshifts
We study the cohomology of symbolic dynamical systems called homshifts: they are the nearest-neighbour $\mathbb{Z}^d$ shifts of finite type whose adjacency rules are the same in every direction. Building on the work of Klaus Schmidt (Pacific J. Math. 170 (1995), no.1, 237-269) we give a necessary and sufficient condition for their cohomological triviality. This condition is expressed in terms of the topology of a natural simplicial complex arising from the shift space which can be analyzed in m…

[2025-08-15 Fri (UTC), 3 new articles found for math.DS Dynamical Systems]
toXiv_bot_toot

[2025-09-15 Mon (UTC), 7 new articles found for math.DS Dynamical Systems]
toXiv_bot_toot

On Irreversibility and Stochastic Systems: Part One
Giorgio Picci
https://arxiv.org/abs/2508.08330 https://arxiv.org/pdf/2508.08330

On Irreversibility and Stochastic Systems: Part One
We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been studied intensively and are shown to exist for stochastic diffusion models. In this setting one has however to face the preliminary justification of stochastic description for physical systems which are described by classical mechanics as inherently deterministic a…

Understanding topological dynamics of hyperbolic dynamical systems via examples
Anima Nagar
https://arxiv.org/abs/2509.08322 https://arxiv.org/pdf/2509.083…

Understanding topological dynamics of hyperbolic dynamical systems via examples
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence of expanding and contracting directions for the associated derivative on some manifold. We study some topological dynamics, essentially the property of `proximality', of two prototype examples of hyperbolic dynamical systems - \emph{Arnold's Cat Map} and \emp…

Crosslisted article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Hausdorff measure of cartesian product of Cantor sets
Siyuan Guo, Taylor Jones

Replaced article(s) found for math.DS. https://arxiv.org/list/math.DS/new
[1/1]:
- Random Young towers and quenched decay of correlations for predominantly expanding multimodal cir...
Matheus M. Castro, Giuseppe Tenaglia