Abstract
We discuss heteroclinic bifurcation in a class of periodically excited planar piecewise smooth systems with discontinuities on finitely many smooth curves intersecting at the origin. Assume that the unperturbed system has a hyperbolic saddle in each subregion, and those saddles are connected by a heteroclinic cycle that crosses every switching curve transversally exactly once. We present a method of Melnikov type to derive sufficient conditions under which the perturbed stable and unstable manifolds intersect transversally. Such transversal intersections imply that the corresponding Poincaré map has a transverse heteroclinic cycle. As applications, we present examples with 2 and 4 switching curves respectively. Our numerical simulations suggest that such transversal intersections result in the appearance of chaotic motions in those example systems.
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This work is supported by NSFC (China) under Grant Numbers 11371264 and 11501549, and China Postdoctoral Science Foundation under Grant Number 2015M571145.
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Shen, J., Du, Z. Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones. Z. Angew. Math. Phys. 67, 42 (2016). https://doi.org/10.1007/s00033-016-0642-2
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DOI: https://doi.org/10.1007/s00033-016-0642-2