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Does the Forced Van der Pol Oscillator Exhibit Irregular Behavior?
Samaira Tibrewal, Soumyajit Seth
https://arxiv.org/abs/2505.22385 https://

Does the Forced Van der Pol Oscillator Exhibit Irregular Behavior?
Nonlinear oscillators are commonly encountered in a wide range of physical and engineering systems, exhibiting rich and complex dynamics. Among these, the Van der Pol oscillator is well known for its self-sustained limit cycle behavior. However, when subjected to external sinusoidal forcing, its dynamics can deviate significantly from this regular behavior. This study explores the emergence of complex dynamical regimes in the sinusoidally forced Van der Pol oscillator, focusing on identifying t…

Conserved Quantities in the Lorenz System
B. A. Toledo
https://arxiv.org/abs/2505.20572 https://arxiv.org/pdf/2505.20572

Conserved Quantities in the Lorenz System
The Lorenz system, a seminal model in chaos theory, is renowned for its complex dynamics and sensitive dependence on initial conditions. This work investigates conserved quantities within the standard Lorenz equations. The system exhibits phase space volume contraction, a characteristic of dissipative systems. Despite the common understanding suggesting an absence of conserved quantities in its typical chaotic parameter regimes, this study demonstrates that the Lorenz system possesses at least …