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


主講人:李曉月 東北師范玖体育直播教授




主講人介紹:一直以來從事應用微分方程方向的研究,主要從事常微分方程和泛函微分方程定性理論,隨機微分方程中的穩定性問題研究。近些年來,對隨機微分方程理論及應用的研究產生濃厚的興趣,研究主要包括隨機微分方程穩定性理論,隨機微分方程數值解以及隨機種群系統的動力學行為等幾方面。在《IMA  Journal of Numerical Analysis》、《SIAM Jounral on Numerical  Analysis》等期刊發表論文30余篇。主持過國家自然科學青年基金項目1項,主持國家自然科學基金面上項目1項。參與國家自然科學基金面上項目子課題1項,吉林省自然科學基金項目1項,參與了多項教育部、國家自然科學基金委項目的研究工作。

內容介紹: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.