主讲人：黄继才  华中师范大学教授

时间：2020年12月6日10：00

地点：腾讯会议 979 174 820

举办单位：数理学院

主讲人介绍：华中师范大学教授、博士生导师。分别于1999年本科、2002年硕士毕业于华中师范大学数学系，2005年获中国科学院数学与系统科学研究院数学所博士学位。黄教授主要从事常微分方程定性理论、分支理论及其应用研究。在J.  Differential Equations、J. Dynam. Differential Equations、SIAM J. Appl. Math.、SIAM  J. Appl. Dyn. Syst.、Bull. Math. Biol. 等期刊发表学术论文三十多篇。主持国家自然科学基金4项。曾获得湖北省自然科学奖三等奖。  

内容介绍：In this talk we study a host-generalist parasitoid model with Holling II  functional response where the generalist parasitoids are introduced to control  the invasion of the hosts. It is shown that the model can undergo a sequence of  bifurcations including cusp, focus and elliptic types degenerate Bogdanov-Takens  bifurcations of codimension three, and a degenerate Hopf bifurcation of  codimension at most two as the parameters vary, and the model exhibits rich  dynamics such as the existence of multiple coexistent steady states, multiple  coexistent periodic orbits, homoclinic orbits, etc. Moreover, there exists a  critical value for the carrying capacity of generalist parasitoids such that:  (i) when the carrying capacity of the generalist parasitoids is smaller than the  critical value, the invading hosts can always persist despite of the predation  by the generalist parasitoids, i.e., the generalist parasitoids cannot control  the invasion of hosts; (ii) when the carrying capacity of the generalist  parasitoids is larger than the critical value, the invading hosts either tend to  extinction or persist in the form of multiple coexistent steady states or  multiple coexistent periodic orbits depending on the initial populations, i.e.,  whether the invasion can be stopped and reversed by the generalist parasitoids  depends on the initial populations; (iii) in both cases, the generalist  parasitoids always persist.