Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model

Abstract In this article multiple and generic bifurcations of planar discrete-time Hindmarsh-Rose oscillator are investigated in detail by bifurcation theory and numerical continuation techniques. Three kinds of one-parameter bifurcation and five kinds of two-parameter bifurcation are studied. Different kinds of critical cases of each bifurcation are computed by inner product method and their corresponding scenario are presented, such as possible transitions between different one-parameter bifurcation points derived from two-parameter bifurcation point. Especially, the bifurcations of higher iterations and the bifurcation distributions of two-parameter bifurcation point are observed.