主講人：劉榮頌 懷俄明大學(xué)教授

時(shí)間：2022年10月14日10：00

地點(diǎn)：騰訊會(huì)議 478 127 447

舉辦單位：數(shù)理學(xué)院

主講人介紹：劉榮頌，美國(guó)懷俄明大學(xué)教授，博士生導(dǎo)師。2006年博士畢業(yè)于加拿大約克大學(xué)，之后在普渡大學(xué)從事博士后研究，2009年入職懷俄明大學(xué)。主要研究興趣在生物數(shù)學(xué)、微分方程、動(dòng)力系統(tǒng)、和他們的交叉領(lǐng)域。研究課題涉及傳染病和生態(tài)系統(tǒng)的數(shù)學(xué)建模、分析及應(yīng)用。先后在SIAM J. Appl. Math., European J. Appl. Math., J. Differential Equations，J. Math. Biol.等權(quán)威雜志發(fā)表論文多篇。

內(nèi)容介紹：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.