Global dynamics of a generalized van der Pol-Duffing system with arbitrary degree

Abstract

We study the global dynamics of a generalized van der Pol-Duffing system in this paper, which has four nonlinear terms with arbitrary degree. This generalized nonlinear system possesses complicated dynamics, including at most three limit cycles, a figure-eight loop, infinitely many heteroclinic bifurcations, Hopf bifurcation, double large limit cycle bifurcation, generalized pitchfork bifurcation and generalized Hopf bifurcation. In addition, these theoretical results are exhibited via numerical simulations.