报 告 人: 王毅中国科学技术大学教授         

报告时间：2021年10月18号(周一)上午10:00-11:00    

地         点：腾讯会议(311420 013)             

报告题目：Generic Poincare-Bendixson Theorem for systems with invariant2-cones and applications to SEIRS epidemic modelse    

报告摘要：

       In this talk, we consider a smooth flow which is monotone w.r.t. a k-cone, aclosed set that contains a linear subspace of dim-k and no linear subspaces ofhigher dimension. We show that orbits with initial data from an open dense(called generic) subset of the phase space are either pseudo-ordered or convergentto equilibria. This covers the celebrated Hirsch's Generic Convergence Theoremin the case k=l, and yields a generic Poincare-Bendixson Theorem for the casek=2. An application to SEIRS-models with nonlinear incidence rates will be presentedto show the possibility of generic convergence to periodic orbits. This is ajoint work with lirui Feng and Jianhong Wu.