Analysis of Dynamic Transitions' Mechanism in the Hindmarsh-Rose System with Method of Geometric Singular Perturbation

The mechanism of typical dynamics is studied on the basis of the geometric singular perturbation theory in this paper. The vital parameters influence on many typical dynamics and the structure of the slow manifold are investigated and stated the mechanism of all kinds of dynamical transitions while these parameters vary. The research of this paper will help to further understand the complex firing patterns in biological nervous system. Moreover, it will enrich the content of nonlinear science.