Traveling wave phenomena of FitzHugh-Nagumo equations and predator-prey systems

讲座名称：Traveling wave phenomena of FitzHugh-Nagumo equations and predator-prey systems

讲座人：杜增吉 教授

讲座时间：12月12日15:00-17:30

地点：腾讯会议 992-314-961

讲座人介绍：

杜增吉，江苏师范大学校长、二级教授、博士生导师，中国数学会奇异摄动专业委员会副理事长，江苏省“333高层次人才”中青年科技领军人才、江苏省“青蓝工程”中青年学术带头人。研究方向为微分方程与动力系统、奇异摄动理论及其应用、生物数学等。在 J. Funct. Anal., J. Nonlinear Sci., J. Differential Equations, J. Math. Biol., Proc. AMS 和《中国科学数学》等数学期刊上发表论文80余篇。主持国家自然科学基金项目6项，参加国家自然科学基金项目重大1项。获得省自然科学奖二等奖、省优秀教学成果奖二等奖和省数学成就奖等，先后担任多个数学SCI杂志编委。

讲座内容：

In this talk, we mainly investigate a coupled FitzHugh -Nagumo (FHN) equation with doubly-diffusive effect and local time delay, which was derived as a simplification of the Hodgkin-Huxley equations for nerve impulse propagation. The singular orbits are constructed by analyzing limit dynamics of the equations in the traveling wave framework by means of phase space analysis. To establish the traveling pulses for the full system, the main analysis relies on exterior differential forms, the geometric singular perturbation theory and Exchange Lemma. We also discuss a three-dimensional diffusive predator-prey system with nonlocal terms and holling II type functional response and obtain the traveling wave.

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