Plant–Herbivore Models with Toxin-Determined Functional Response

主讲人：刘荣颂 怀俄明大学教授

时间：2022年10月14日10：00

地点：腾讯会议 478 127 447

举办单位：数理学院

主讲人介绍：刘荣颂，美国怀俄明大学教授，博士生导师。2006年博士毕业于加拿大约克大学，之后在普渡大学从事博士后研究，2009年入职怀俄明大学。主要研究兴趣在生物数学、微分方程、动力系统、和他们的交叉领域。研究课题涉及传染病和生态系统的数学建模、分析及应用。先后在SIAM J. Appl. Math., European J. Appl. Math., J. Differential Equations，J. Math. Biol.等权威杂志发表论文多篇。

内容介绍：First, a system of ODEs is considered which models the plant–herbivore interactions mediated by a toxin-determined functional response. The new functional response is a modification of Holling type II functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through Hopf bifurcations and homoclinic bifurcation. The results are obtained not only analytically but also confirmed and extended numerically. Then we focus particularly on the fact that toxin concentration often varies with the age of twig segments. The model incorporates the fact that the woody internodes of the youngest segments of the twigs of the deciduous angiosperm species that these hares prefer to eat are more defended by toxins than the woody internodes of the older segments that subtend and support the younger segments. Basic mathematical properties of the model are established together with upper and lower bounds on the solutions. Necessary and sufficient conditions are found for the linear stability of the equilibrium in which the hare is extinct, and sufficient conditions are found for its global stability.