题目：Complex dynamics in a delay differential equation with two delays in tick growth with diapause
摘要：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.
时间：2021年9月30日（周四），10:00-11:30
地点： 腾讯会议ID: 243-636-101
主讲人: 汪翔升教授（美国路易斯安那大学拉法叶分校）
主讲人简介：汪翔升，美国University of Louisiana at Lafayette大学教授、博导。于2009年获得香港城市大学博士学位；2009-2013年先后在香港城市大学，加拿大York大学、Memorial University of Newfoundland大学从事博士后研究工作；主要研究渐近分析、微分动力系统、生物数学和计算数学。迄今为止已在Advances in Mathematics、J. Math. Pures Appl.、SIAM J. Control and Optimization、Studies in Applied Mathematics、JDE、JDDE、BMB、JMB、JTB、MBS等国际专业权威期刊上发表学术论文五十余篇。
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