基于几何奇异摄动法分析HR系统中参数导致的动力学转迁机制

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

本文首先考察了系统中关键参数对系统慢变流形结构的影响,从而阐明这些参数变化时导致各种典型的动力学现象和动力学转迁的内在机制。本文的研究将有助于进一步理解生物神经系统中复杂的放电现象,同时也丰富了非线性科学的内容。

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.