Speaker: Wang Yi, Professor, School of Mathematical Sciences, University of Science and Technology of China

Date: November. 4, 2021

Time: 16:30-17:30

Location: Tencent Meeting, ID: 886 815 093

Sponsor: School of Mathematics, Shandong University

Abstract:

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 Poincaré-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.

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https://www.view.sdu.edu.cn/info/1020/158578.htm