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报告题目：Maximum number of limit cycles of the piecewise linear Li\'enard system with three zones

报告人：陈和柏 教授

报告时间：2025年12月25日10:00-12:00

报告地点：浪live 210会议室

邀请人：贾曼

邀请单位：浪live

报告摘要： For the piecewise linear Li\'enard system $\dot x=F(x)-y$, $\dot y=x$, where $F(x)$ is a continuous piecewise linear function with $n$ fold points, the question of how many limit cycles that such a system can have has been a classical and open problem in differential equations and dynamical systems. Nowadays, we only know the answer for the case $n=1$. For the cases $n\geq2$, the problem still remains open. This paper aims to give an affirmative answer for the case $n=2$ of this open problem, i.e., the maximum number of limit cycles of the continuous piecewise linear function with 2 fold points is 2. This system exhibits abundantly interesting and rich dynamics, including the generalized Hopf bifurcation, boundary equilibrium bifurcation, grazing limit cycle bifurcation, and double limit cycle bifurcation, which may have potential interdisciplinary applications.

报告人简介：陈和柏,博士,中南大学浪live 教授、博导, 从事微分方程与动力系统的教学和研究, 主要研究兴趣为光滑及非光滑微分方程的定性理论与分岔理论。获四川大学数学学士和硕士学位、西南交通大学力学博士学位，之后应邀赴英国帝国理工学院、诺丁汉大学短访。在《Advances in Mathematics》、《Mathematiche Annalen》、《Journal of the London Mathematical Society》、《Nonlinearity》、《Journal of Differential Equations》、《Journal of Nonlinear Science》、 《SIAM Journal on Mathematical Analysis》、《Physica D》、《Annali di Matematica Pura ed Applicata》等国际重要期刊以一作或通讯身份发表SCI学术论文70多篇；获得国家优青项目资助，主持了相关的国家面上和青年基金。现任中国数学会T3杂志《Annals of Applied Mathematics》的Associate Editor。

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