Replication of Li-Yorke Chaos Near a Homoclinic Orbit
Marat Akhmet, Michal Fe\v{c}kan, Mehmet Onur Fen, Ardak Kashkynbayev
TL;DR
This paper demonstrates the presence of Li-Yorke chaos near a homoclinic orbit in a Duffing oscillator through chaotic perturbations, supported by simulations and control methods for stabilization.
Contribution
It introduces a novel approach to proving Li-Yorke chaos near homoclinic orbits using chaotic perturbations and applies control techniques to stabilize motions.
Findings
Chaos confirmed near homoclinic orbit in Duffing oscillator
Chaotic perturbations effectively induce chaos
Control methods stabilize almost periodic motions
Abstract
We prove the presence of chaos near a homoclinic orbit in the modified Li-Yorke sense [10] by implementing chaotic perturbations. A Duffing oscillator is considered to show the effectiveness of our technique, and simulations that support the theoretical results are depicted. Ott-Grebogi-Yorke and Pyragas control methods are used to stabilize almost periodic motions.
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Taxonomy
TopicsChaos control and synchronization · Nonlinear Dynamics and Pattern Formation · Quantum chaos and dynamical systems