Asymptotic Properties of Multi-species Lotka-Volterra Models with Regime Switching Involving


主讲人:李晓月 东北师范大学教授




主讲人介绍:一直以来从事应用微分方程方向的研究,主要从事常微分方程和泛函微分方程定性理论,随机微分方程中的稳定性问题研究。近些年来,对随机微分方程理论及应用的研究产生浓厚的兴趣,研究主要包括随机微分方程稳定性理论,随机微分方程数值解以及随机种群系统的动力学行为等几方面。在《IMA ?Journal of Numerical Analysis》、《SIAM Jounral on Numerical ?Analysis》等期刊发表论文30余篇。主持过国家自然科学青年基金项目1项,主持国家自然科学基金面上项目1项。参与国家自然科学基金面上项目子课题1项,吉林省自然科学基金项目1项,参与了多项教育部、国家自然科学基金委项目的研究工作。

内容介绍:This work focuses on multi-species Lotka-Volterra models with regime switching ?modulated by a continuous-time Markov chain involving a small parameter. The ?small parameter is used to reflect different rates of the switching among a ?large number of states representing the discrete events. Using perturbed ?Lyapunov function methods and the structure of the limit system as a bridge, ?stochastic permanence and extinction are obtained. Sufficient conditions under ?which the measures of the original system converge to the invariant measure of ?that of the limit system are provided. A couple of examples and numerical ?simulations are given to illustrate our results.