Abstract
The aim of this paper is to give the bifurcation diagram and all global phase portraits in the Poincaré disc of a generalized Bogdanov-Takens system with arbitrary degree. Moreover, the system has abundant nonlinear phenomena, such as double limit cycle bifurcation, Hopf bifurcation, homoclinic bifurcation, heteroclinic bifurcation, and so on. Notice that the nonlinear phenomena of the system are more abundant and more complex than the classic Bogdanov-Takens system.
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