勷勤数学•专家报告

题      目：Global dynamics and bifurcation for a discontinuous oscillator with irrational nonlinearity

报  告  人：王佳伏 教授  (邀请人：余虓)

                                             长沙理工大学

时      间：7月14日  17：00-18：00

地     点：数科院西楼111报告厅

报告人简介:

       王佳伏，博士，教授，长沙理工大学博士生导师，湖南省数学会常务理事。主要从事非光滑动力系统的定性理论与分支理论、生物数学、神经网络等方面的研究。主持国家自然科学基金项目3项、湖南省自然科学基金项目2项，其研究成果发表在SIAM Journal on Applied Mathematics、Journal of Differential Equations、Physica D等学术期刊上。

摘      要：

        In this talk, we focus on global dynamics and bifurcation for a discontinuous oscillator, showing the transition of dynamics between the piecewise smooth system and the piecewise linear system. The existence of one or three equilibrium sets is proven by the approach of Filippov. Based on non-smooth Lyapunov functions and their set-valued derivatives, asymptotical stability especially finite-time asymptotical stability is shown for the equilibrium sets. In particular, some conditions are established guaranteeing the uniqueness of an equilibrium set and its global finite-time asymptotical stability. Making use of the parametric representation, codimension-one bifurcation curves and a codimension-two bifurcation point are obtained.

        欢迎老师、同学们参加、交流！