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Homoclinic cycles coexisting and chaos in three-dimensional piecewise linear systems

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  • Xu, Wenchao

Abstract

This paper establishes sufficient conditions for the accurate detection of coexisting homoclinic cycles and chaos in a class of three-dimensional piecewise affine systems. Through a rigorous analysis of the Poincaré map, we analytically demonstrate that chaotic dynamics in the considered system emerge from coexisting nonsymmetrical homoclinic cycles. This intriguing dynamical phenomenon stands in stark contrast to smooth systems, where chaos cannot be induced by an asymmetric pair of homoclinic cycles connecting the same equilibrium point. To validate and illustrate our theoretical findings, we present a concrete example with numerical simulations that verify the predicted behavior.

Suggested Citation

  • Xu, Wenchao, 2026. "Homoclinic cycles coexisting and chaos in three-dimensional piecewise linear systems," Chaos, Solitons & Fractals, Elsevier, vol. 208(P3).
    • Handle: RePEc:eee:chsofr:v:208:y:2026:i:p3:s0960077926004066
    DOI: 10.1016/j.chaos.2026.118265
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