講座名稱：Traveling wave phenomena of FitzHugh-Nagumo equations and predator-prey systems

講座人：杜增吉 教授

講座時(shí)間：12月12日15:00-17:30

地點(diǎn)：騰訊會(huì)議 992-314-961

講座人介紹：

杜增吉，江蘇師范大學(xué)校長(zhǎng)、二級(jí)教授、博士生導(dǎo)師，中國(guó)數(shù)學(xué)會(huì)奇異攝動(dòng)專業(yè)委員會(huì)副理事長(zhǎng)，江蘇省“333高層次人才”中青年科技領(lǐng)軍人才、江蘇省“青藍(lán)工程”中青年學(xué)術(shù)帶頭人。研究方向?yàn)槲⒎址匠膛c動(dòng)力系統(tǒng)、奇異攝動(dòng)理論及其應(yīng)用、生物數(shù)學(xué)等。在 J. Funct. Anal., J. Nonlinear Sci., J. Differential Equations, J. Math. Biol., Proc. AMS 和《中國(guó)科學(xué)數(shù)學(xué)》等數(shù)學(xué)期刊上發(fā)表論文80余篇。主持國(guó)家自然科學(xué)基金項(xiàng)目6項(xiàng)，參加國(guó)家自然科學(xué)基金項(xiàng)目重大1項(xiàng)。獲得省自然科學(xué)獎(jiǎng)二等獎(jiǎng)、省優(yōu)秀教學(xué)成果獎(jiǎng)二等獎(jiǎng)和省數(shù)學(xué)成就獎(jiǎng)等，先后擔(dān)任多個(gè)數(shù)學(xué)SCI雜志編委。

講座內(nèi)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.

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院