主講人：汪翔升 美國(guó)路易斯安娜大學(xué)副教授

時(shí)間：2022年5月16日10：00

地點(diǎn)：騰訊會(huì)議 145 865 637

舉辦單位：數(shù)理學(xué)院

主講人介紹：汪翔升副教授畢業(yè)于香港城市大學(xué)和中國(guó)科學(xué)技術(shù)大學(xué)聯(lián)合高等研究中心。他的研究興趣包括漸近分析和生物數(shù)學(xué)等交叉學(xué)術(shù)領(lǐng)域，最近五年在A(yíng)dv. Math., J. Differential Equations, J. Math. Biol., J. Math. Pures. Appl., SIAM J. Control Optim.等雜志上發(fā)表論文二十余篇。

內(nèi)容介紹：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.