报告题目：The rhythm of ticks ticking: the parametric trigonometric functions and delay differential equations with diapause delays

报告人：吴建宏 教授 加拿大约克大学

邀请人：吴事良

报告时间：2022年7月18日（周日）9：00

腾讯会议ID：464 449 228

报告人简介：吴建宏，现任加拿大应用数学首席教授(Canada Research Chair)，加拿大约克大学伟德国际BETVlCTOR终身教授，湖南大学客座教授。吴建宏教授是传染病建模和大数据信息分析的联合主编，同时是《J. Mathematical Biology》和《IEEE Transactions on the Pattern Analysis and Machine Intelligence》等期刊的编委会成员；担任菲尔兹研究所委托的加拿大国家COVID-19大流行快速响应建模工作组的负责人，是省（安大略省）和联邦（加拿大）建模专家组成员。在Kluwer、AMS/Fields、Springer、Wiley等出版社出版专著8部，编著14部，发表学术论文350多篇。研究方向包括动力系统、神经网络和模式识别、生物数学和流行病学。获得了包括加拿大女王钻石禧功勋章、约克大学终身杰出特聘教授、终身Fields Institute Fellow、加拿大华人专业人士杰出成就奖、加拿大新先锋科技奖等在内的10余项学术成就奖。

报告摘要：The population dynamics of ticks is responsible for a range of tick-borne diseases. Diapause is an important adaptive mechanism for ticks in respond to variable climate. Incorporating this physiological mechanism into a tick population dynamics model results in a delay differential system. We consider the mechanistic model with the development diapause by both larvae and nymph ticks. Using the concept of parametric trigonometric functions, we derive an explicit formula of the critical diapause portion for the Hopf bifurcation to take place. We obtain global existence of periodic solutions by using the equivalent-degree based global Hopf bifurcation theory, coupled with an application of the Li–Muldowney technique to rule out periodic solutions with period 3τ.