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Global Bifurcation for a Class of Planar Filippov Systems with Symmetry

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Abstract

In this paper global bifurcations for a class of planar Filippov systems with symmetry, namely the Filipov-van der Pol oscillator are studied. First, we discuss qualitative properties of equilibria (including equilibria at infinity), where the origin is a pseudo equilibrium, and some equilibria at infinity are discussed by Briot-Bouquet transformations and constructing generalized normal sectors. For all cases we give sufficiently and necessarily conditions of limit cycles. Every global phase portrait is given as well as the complete global bifurcation diagram (including generalized Hopf bifurcation et al.).

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Acknowledgments

The author is grateful to the Reviewers for their careful suggestions and comments. This work is supported by the National Natural Science Foundations of China 11572263, 11272268, and 2015 Cultivation Program for the Excellent Doctoral Dissertation of Southwest Jiaotong University.

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  1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, Sichuan, 610031, People’s Republic of China

    Hebai Chen

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  1. Hebai Chen
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Chen, H. Global Bifurcation for a Class of Planar Filippov Systems with Symmetry. Qual. Theory Dyn. Syst. 15, 349–365 (2016). https://doi.org/10.1007/s12346-015-0178-4

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