Tootfinder

This https://arxiv.org/abs/2503.03758 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Classical periodic orbits in extended phase space for spherical harmonic oscillator with spin-orbit coupling
A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables derived by semiclassical approximation to the spin coherent state path integral representation. In addition to the diametric and two circular PO families with frozen spin, solutions that bridge two circular POs are found in which orbital motion is coupled to…

This https://arxiv.org/abs/2411.16699 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Bistability and chaos in the discrete two-gene Andrecut-Kauffman model
We conduct numerical analysis of the 2-dimensional discrete-time gene expression model originally introduced by Andrecut and Kauffman (Phys. Lett. A 367: 281-287, 2007). In contrast to the previous studies, we analyze the dynamics with different reaction rates $α_1$ and $α_2$ for each of the two genes under consideration. We explore bifurcation diagrams for the model with $α_1$ varying in a wide range and $α_2$ fixed. We detect chaotic dynamics by means of the positive maximum Lyapunov expo…

This https://arxiv.org/abs/2308.00060 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

An Invitation to Number-Conserving Cellular Automata
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional number-conserving automata. Here I describe in greater detail how one can simulate the automata on a computer and how to find interesting rules. I show several rules that I have found this way and also some theorems about the space of number-conserving automat…

This https://arxiv.org/abs/2108.12692 has been replaced.
link: https://scholar.google.com/scholar?q=a

Integrable dynamics in projective geometry via dimers and triple crossing diagram maps on the cylinder
We introduce twisted triple crossing diagram maps, collections of points in projective space associated to bipartite graphs on the cylinder, and use them to provide geometric realizations of the cluster integrable systems of Goncharov and Kenyon constructed from toric dimer models. Using this notion, we provide geometric proofs that the pentagram map and the cross-ratio dynamics integrable systems are cluster integrable systems. We show that in appropriate coordinates, cross-ratio dynamics is d…

This https://arxiv.org/abs/2406.15408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is t…

On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain
I. T. Habibullin, A. R. Khakimova
https://arxiv.org/abs/2505.20786

On the construction of solutions of the Davey--Stewartson I equation using an open Toda chain
An effective method for constructing explicit solutions to the Davey--Stewartson type integrable equations is discussed based on the use of a dressing chain. The application of the method is exemplified by the equation DS I, for which a new class of explicit solutions is constructed, containing freedom in two arbitrary functions. In this case the generalized Toda lattice corresponding to the simple Lie algebra $A_2$ is used as a dressing chain.

This https://arxiv.org/abs/2406.15408 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Effects of a Vanishing Noise on Elementary Cellular Automata Phase-Space Structure
We investigate elementary cellular automata (ECA) from the point of view of (discrete) dynamical systems. By studying small lattice sizes, we obtain the complete phase space of all minimal ECA, and, starting from a maximal entropy distribution (all configurations equiprobable), we show how the dynamics affects this distribution. We then investigate how a vanishing noise alters this phase space, connecting attractors and modifying the asymptotic probability distribution. What is interesting is t…

This https://arxiv.org/abs/2411.05607 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Suppressing parametric resonance of a Hyperloop vehicle using a parametric force
In this paper, we study the stability of a simple model of a Hyperloop vehicle resulting from the interaction between electromagnetic and aeroelastic forces for both constant and periodically varying coefficients (i.e., parametric excitation). For the constant coefficients, through linear stability analysis, we analytically identify three distinct regions for the physically significant equilibrium point. Further inspection reveals that the system exhibits limit-cycle vibrations in one of these …

A system of 2 nonlinearly coupled ODEs which is explicitly solvable and possibly isochronous provided its coefficients are suitably restricted
Fabio Briscese, Francesco Calogero, Farrin Payandeh
https://arxiv.org/abs/2505.24370

A system of 2 nonlinearly coupled ODEs which is explicitly solvable and possibly isochronous provided its coefficients are suitably restricted
In this paper we discuss some remarkable properties of the autonomous system of 2 first-order Ordinary Differential Equations (ODEs), which equates the derivatives $\dot{x}_n(t)$ ($n = 1, 2$) of the 2 dependent variables $x_n(t)$ to the ratios of polynomials (with constant coefficients) in the 2 variables $x_n (t)$: each of the 2 (a priori different) polynomials $P_3^{(n)}(x_1, x_2)$ in the 2 numerators is of degree 3; the 2 denominators are instead given by the same polynomial $P_1(x_1, x_2)$ …

A State of the Art on Recent Progress and Emerging Challenges on Energy Transfer Between Vibrating Modes Under an External Mechanical Force With Time-Varying Frequency From 2020 to 2025
Jose Manoel Balthazar, Jorge Luis Palacios Felix, Mauricio A. Ribeiro, Angelo Marcelo Tusset, Jeferson Jose de Lima, Vinicius Piccirillo, Julijana Simonovic, Nikola D. Nevsic, Marcos Varanis, Clivaldo de Oliveira, Raphaela C. Machado, Gabriella O M Oliveira

A State of the Art on Recent Progress and Emerging Challenges on Energy Transfer Between Vibrating Modes Under an External Mechanical Force With Time-Varying Frequency From 2020 to 2025
In this paper, we discuss an example of current importance with a future perspective in engineering, in which excitation sources always have limited power, limited inertia, and their frequencies vary according to the instantaneous state of the vibrating system. Practical examples of non-ideal systems are considered. The most common phenomenon for this kind of system is discussed. The period considered is from 2020 to 2025. The specific properties of various models are also discussed. Directions…