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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