报告题目：Generic Poincare-Bendixson Theorem for systems with invariant 2-cones and applications to SEIRS-models

报 告 人：王毅教授（中国科学技术大学）

报告时间：2022年4月1日9:30-11:30

报告地点：腾讯会议（750995076）

报告摘要：In this talk, we will review the fundamental theory, as well as recent progress, of monotone dynamical systems. We further consider a smooth flow with an invariant $k$-cone, a closed set that contains a linear subspace of dim-$k$ and no linear subspaces of higher dimension. We show that orbits with initial data from an open dense (called generic) subset of the phase space are either pseudo-ordered or convergent to equilibria. For $k=1$, this covers the celebrated Hirsch's Generic Convergence Theorem in monotone dynamical systems. For $k=2$, it yields an iteresting generic Poincare-Bendixson Theorem. An application to SEIRS-models with nonlinear incidence rates will be presented to show the possibility of generic convergence to periodic orbits. This talk is based on a series of joint works with Lirui Feng, Jianhong Wu and Jinxiang Yao.

个人简介：王毅，中国科技大学数学科学学院教授、博士生导师。2002年获得中国科技大学理学博士学位。曾应邀对美国佐治亚理工学院、芬兰赫尔辛基大学、美国明尼苏达大学IMA研究所长期学术访问，现任中国科大数学科学学院副院长。主要研究领域为微分方程与动力系统，先后在包括JEMS、 Adv. Math、 Proc. London Math. Soc.、SIAM J. Math. Anal.、JDE、Tans. Amer. Math. Soc.等国际杂志发表论文30余篇。2004年入选全国百篇优秀博士论文，2007年入选教育部新世纪优秀人才支持计划，2018年获基金委国家杰出青年科学基金资助。