Shilnikov Chaos in Oscillators with Huygens Coupling-Reference-Cited by-同舟云学术

Shilnikov Chaos in Oscillators with Huygens Coupling

Published:2014-08 Issue:08 Volume:24 Page:1440007
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

Belykh Vladimir N.¹²,Pankratova Evgeniya V.¹

Affiliation:

1. Department of Mathematics, Volga State Academy, 5A, Nesterov Str., Nizhny Novgorod, 603950, Russia

2. Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23, Gagarin Ave., Nizhny Novgorod, 603950, Russia

Abstract

We consider van der Pol–Duffing oscillators coupled via a two-dimensional linear system, representing Huygens coupling. We demonstrate that two identical synchronized oscillators can have chaotic movements and exhibit Shilnikov chaos. We rigorously prove the existence of a homoclinic orbit of a saddle-focus and a symmetrical heteroclinic contour of two saddle-foci, leading to the appearance of chaos via the Shilnikov saddle-focus bifurcation. We also support our analytical results with numerical simulations, revealing the main signature of Shilnikov chaos, the coexistence of chaotic and regular attractors with riddled basins of attraction, including wild attractors.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218127414400070

Reference12 articles.

1. V. N. Belykh, Advances in the Mathematical Sciences, American Mathematical Society Translations 200 (2000) pp. 51–62.

2. Huygens's clocks

3. W. T. Oud, H. Nijmeijer and A. Yu. Pogromsky, Group Coordinations and Control, eds. K. Y. Pettersen, J. T. Gravdahl and H. Nijmeijer (Springer, Berlin, 2006) pp. 66–76.

Cited by 8 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Self-balancing characteristics of three self-synchronous linear motion mechanical oscillators;Structures;2023-09

2. Homoclinic Orbits and Chaos in Nonlinear Dynamical Systems: Auxiliary Systems Method;Lobachevskii Journal of Mathematics;2021-12

3. Shilnikov Saddle-Focus Homoclinic Orbits from Numerics: Higher Dimensions;Journal of Dynamics and Differential Equations;2021-01-25

4. When three is a crowd: Chaos from clusters of Kuramoto oscillators with inertia;Physical Review E;2020-06-18

5. The Coexisting Behaviors on the Boundary of a Duffing-like Oscillator with Signum Nonlinearity and Its FPGA-Based Implementation;International Journal of Bifurcation and Chaos;2020-05