报告题目：Maximum number of limit cycles of the discontinuous piecewise linear Lienard system with one switching line

报告人：陈和柏 教授

报告时间：2026年6月14日16:00-18:00

报告地点：数统学院208

邀请人：贾曼

邀请单位：福州大学数学与统计学院

报告摘要：For a discontinuous piecewise linear Li\'{e}nard system $\dot{x} = F(x)-y$, $\dot{y} = x$, where $F(x)$ is an $n$ piecewise linear function, the question of how many limit cycles it can possess has been a classical and open problem in the theory of differential equations and dynamical systems.Up to now, this problem remains unresolved in general.This paper aims to provide an answer for the case $n=1$ of this open problem.We prove that the maximum number of limit cycles for such a system with one discontinuity is $2$.To this end, we start with the global phase portraits and bifurcation diagrams of the discontinuous piecewise linear Li\'enard system for the case $n=1$.The system exhibits a wealth of interesting and rich dynamics, including the coexistence of crossing and sliding cycles, grazing limit cycle bifurcations, and double limit cycle bifurcations, which may have potential interdisciplinary applications.

报告人简介：陈和柏,博士,中南大学数学与统计学院教授、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。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(2023)资助，主持了相关的国家面上(2021,2025)和青年基金(2018)。现任中国数学会T3杂志《Annals of Applied Mathematics》的Associate Editor。

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