Bifurcation of limit cycles at infinity in piecewise polynomial systems

By Ting Chen, Lihong Huang, Pei Yu, Wen-Yang Huang. Nonlinear Analysis: Real World Applications, 2018

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Abstract In this paper, we study bifurcation of limit cycles from the equator of piecewise polynomial systems with no singular points at infinity. We develop a method for computing the Lyapunov constants at infinity of piecewise polynomial systems. In particular, we consider cubic piecewise polynomial systems and study limit cycle bifurcations in the neighborhood of the origin and infinity. Moreover, an example is presented to show 11 limit cycles bifurcating from infinity.

Subfields: Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/eb01158c16eb8ef6395c57c8485b01323e1070c1