Complex dynamics in a delay differential equation with two delays in tick growth with diapause

主讲人：汪翔升 美国路易斯安娜大学副教授

时间：2022年5月16日10：00

地点：腾讯会议 145 865 637

举办单位：数理学院

主讲人介绍：汪翔升副教授毕业于香港城市大学和中国科学技术大学联合高等研究中心。他的研究兴趣包括渐近分析和生物数学等交叉学术领域，最近五年在Adv. Math., J. Differential Equations, J. Math. Biol., J. Math. Pures. Appl., SIAM J. Control Optim.等杂志上发表论文二十余篇。

内容介绍：We consider a delay differential equation for tick population with diapause, derived from an age-structured population model, with two time lags due to normal and diapause mediated development. We derive threshold conditions for the global asymptotic stability of biologically important equilibria, and give a general geometric criterion for the appearance of Hopf bifurcations in the delay differential system with delay-dependent parameters. By choosing the normal development time delay as a bifurcation parameter, we analyze the stability switches of the positive equilibrium, and examine the onset and termination of Hopf bifurcations of periodic solutions from the positive equilibrium. Under some technical conditions, we show that global Hopf branches are bounded and connected by a pair of Hopf bifurcation values. This allows us to show that diapause can lead to the occurrence of multiple stability switches, coexistence of two stable limit cycles, among other rich dynamical behaviours.