报告题目：Local Stability and Hopf Bifurcations Analysis of the Muthuswamy-Chua-Ginoux System

报告人：田育周 （清华大学 博士后）

报告时间：2022年6月1日（周三）10：30-11：30

报告地点：腾讯会议：551572934

主办单位：002cc白菜资讯

主讲/发言人：田育周，分别于广东技师师范学院和中山大学获理学学士和理学博士学位，现为清华大学数学系博士后。主要研究方向为常微分方程及其应用。以第一作者或通讯作者在 《Physica D》、《Nonlinear Anal.》、《Z. Angew. Math. Phys.》、《J. Math. Phys.》等学术期刊发表论文 11 篇。

内容简介 The 3-dimensional Muthuswamy-Chua-Ginoux (MCG, for short) circuit system based on a thermistor is a generalization of the classical Muthuswamy-Chua circuit differential system. In this work, we study local stability and Hopf bifurcations of the MCG circuit system depending on 8 parameters. The emerging of limit cycles under zero-Hopf bifurcation and Hopf bifurcation is investigated in detail by using the averaging method and the center manifolds theory, respectively. We provide sufficient conditions for a class of the circuit systems to have a prescribed number of limit cycles bifurcating from the zero-Hopf equilibria by making use of the third order averaging method, as well as the methods of Gr\"obner basis and real solution classification from symbolic computation. After, the classical Hopf bifurcation of the circuit system is analyzed by computing the first three focus quantities near the Hopf equilibria.