Generic Poincare-Bendixson Theorem for systems with invariant 2-cones and applications

主讲人：王毅  中国科学技术大学教授

时间：2021年10月18日10：00

地点：腾讯会议 311 420 013

举办单位：数理学院

主讲人介绍：王毅，中国科学技术大学数学科学学院教授。曾入选全国百篇优秀博士论文。主要感兴趣领域为非线性微分方程，无限维动力系统及生物数学。  

内容介绍：In this talk, we consider a smooth flow which is monotone w.r.t. a 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. This covers the celebrated Hirsch's Generic  Convergence Theorem in the case k=1, and yields a generic Poincare-Bendixson  Theorem for the case k=2. An application to SEIRS-models with nonlinear  incidence rates will be presented to show the possibility of generic convergence  to periodic orbits. This is a joint work with Lirui Feng and Jianhong Wu.