Speaker：Yi Wang（University of Science Technology of China）

Time：2021-11-05 16:00

Location： Tencent Meeting ID：744 346 862（No Password）

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 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.