报告题目：An efficient approach for analyzing higher-codimension bifurcation problems

报告人：郁培教授，加拿大西安大略大学

报告时间：2024年6月7日（周五）10:00-11:00

报告地点：20-308

报告摘要：In solving real world systems for higher-codimension bifurcation problems, one often faces the difficulty in computing the normal forms with unfolding for higher-codimension Hopf and Bogdanov-Takens bifurcations. The difficulty is not only coming from tedious computation, but also due to the restriction on the system parameters, which frequently leads to failure of the conventional approach used in the computation even for simple 2-dimensional nonlinear dynamical systems. In this talk, we use a simple 2-dimensional epidemic model, for which the conventional approach fails in analyzing the stability of limit cycles arising from Hopf bifurcation, to illustrate how our method can be efficiently applied to determine the codimension of Hopf bifurcation. Further, we apply the simplest normal form theory to consider codimension-3 Bogdanov-Takens bifurcation and present an efficient one-step transformation approach, compared with the classical six-step transformation approach to demonstrate the advantage of our method.

报告人简介：郁培，教授，博士生导师，他在上海交通大学获得学士学位，在滑铁卢大学获得硕士和博士学位，曾获安大略省省长杰出研究奖，主要研究方向包括非线性和混沌动力系统、稳定性和分岔、微分方程计算、生物数学以及在物理和工程系统中的应用。郁培教授（作为作者或合著者）出版了3部专著和200余篇期刊论文，目前是一些国际期刊的编辑委员会成员，并担任多所大学的客座教授。