【Lecture】Travelling pulses in a coupled FitzHugh-Nagumo equation

Publisher:钱玲丽Release time:2020-01-09Browse the number:10

主题:   Travelling pulses in a coupled FitzHugh-Nagumo equation主讲人:   张祥地点:   松江校区2号学院楼理学院454会议室时间:   2020-01-09 13:00:00组织单位:   理学院


张祥,上海交通大学特聘教授(博士生导师、二级教授、享受国务院特殊津贴专家),欧洲科学与艺术院院士。曾获教育部新世纪优秀人才、上海市曙光学者和上海市浦江学者。主要从事动力系统的定性、分支和可积理论的研究。所得结果部分解决了动力系统领域长期遗留的困难的公开问题和猜想,主要结果发表在American J. Math., Comm. Math. Phys., J.Functional Analysis, J. Nonlinear Sciences 和J. DifferentialEquations等国际一流数学杂志上。目前担任中国数学会奇异摄动专业委员会主任、中国数学会理事,以及两个国际SCI杂志Qualitative Theoryof Dynamical Systems和International J. Bifurcation and Chaos的Associate编委等。


We introduce our recent results on travelling pulse of a coupledFitzHugh-Nagumo (FHN) equation with a parameter in [0, 1].  When the parameter isin  (0, 1/2),the existence of travelling pulses of this equation was proved in2013. Here we adopt a new approach to obtain the existence of the travellingpulse of the same equation for the parameter in [0, 1/2), which includes thedegenerate case 0, where we also show that the pulse does not exhibit aoscillatory tail at the homoclinic orbit when the time goes to infinity,whereas the classical FHN equation could have a oscillatory tail of thetraveling pulse depending on the choice of the parameters of the system.Finally we present an explanation on why travelling pulses cannot exist whenthe parameter in [1/2, 1].