Codimension-two bifurcation analysis in two-dimensional Hindmarsh–Rose model
Xuanliang Liu· Shenquan Liu

In this paper, we analyze the codimension-2 bifurcations of equilibria of a two-dimensional Hind-marsh–Rose model. By using the bifurcation methods and techniques, we give a rigorous mathematical anal-ysis of Bautin bifurcation. The main result is that no more than two limit cycles can be bifurcated from the equilibrium via Hopf bifurcation; sufficient conditions for the existence of one or two limit cycles are ob-tained. This paper also shows that the model under-goes a Bogdanov–Takens bifurcation which includes a saddle-node bifurcation, an Andronov–Hopf bifurca-tion, and a homoclinic bifurcation. In some case, the globally asymptotical stability is discussed.

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