主講人：王毅  中國(guó)科學(xué)技術(shù)大學(xué)教授

時(shí)間：2021年10月18日10：00

地點(diǎn)：騰訊會(huì)議 311 420 013

舉辦單位：數(shù)理學(xué)院

主講人介紹：王毅，中國(guó)科學(xué)技術(shù)大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授。曾入選全國(guó)百篇優(yōu)秀博士論文。主要感興趣領(lǐng)域?yàn)榉蔷€(xiàn)性微分方程，無(wú)限維動(dòng)力系統(tǒng)及生物數(shù)學(xué)。  

內(nèi)容介紹：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.