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Study on the codimension of Hopf and Bogdanov-Takens bifurcations

发布时间：2021-12-20 作者：浏览次数：

Speaker:	郁培	DateTime:	2021年12月23日（周四）上午8：30-9：30
Brief Introduction to Speaker: 郁培教授，Western University		Place:	腾讯会议：559601694
Abstract:The analysis of Hopf and Bogdanov-Takens (B-T) bifurcations plays a very important role in the study of nonlinear dynamical systems. A common task of the study is to determine the codimension of the bifurcation and to derive the associated normal form, which is not easy for higher-codimension bifurcations, in particular in order to establish the relation between the original system and the simplified system (normal form). In this talk, we present several biological systems and show how to determine the codimension of Hopf and B-T bifurcations. We will introduce the classical "6-step" transformation approach for codimension-3 B-T bifurcation, and our "1-step" transformation approach, based on the simplest normal form (SNF) theory, for higher-codimension B-T bifurcations. Comparison on these two methods will be briefly discussed.