题 目：Basins of attraction and paired Hopf bifurcations for delay differential equations with bistable nonlinearity anddelay-dependent coefficient

报告人：王林教授（University of New Brunswick--Canada）

报告时间：2023年5月25日星期四 晚上19：30-21：30

地点：腾讯会议：753-808-715

主办单位：广西师范大学数学与统计学院

报告摘要：We consider a class of delay differential equations with bistable nonlinearity, in which the trivial equilibrium may coexist with two positive equilibria. Despite the difficulty caused by  delay and bistable nonlinearity, we give a rather complete  description on the dynamics including global stability, semi-stability, bistability and Hopf bifurcation. For the case where the stable trivial equilibrium coexists with a stable positive equilibrium, we obtain two delay-dependent intervals as subsets of basins of attraction of two stable equilibria. These subsets are sharp in some sense. Using delay as the bifurcation parameter, we analytically show  that the number of local Hopf bifurcation values is finite and these local Hopf bifurcation values are neatly paired. A Nicholson's blowflies equation with Allee effect is used to illustrate our general results. Through this example, we show that delay can induce  stability switches, symmetric  transitions among multitype bistability and robust phase-transitions for long transients.

报告人简介：王林教授，博士毕业于加拿大纽芬兰纪念大学，加拿大麦克马斯特大学、大不列颠哥伦比亚大学博士后。现加拿大University of New Brunswick终身教授。主要从事应用数学研究，其研究涉及生物数学、生态学、神经网络、优化控制、流行病学等多个领域。主持和参与加拿大国家自然与工程基金、加拿大MITACS基金重点项目、加拿大自然与工程战略项目等6项。已在SIAM- J. Appl. Math.、Journal of Differential Equations、Journal of Mathematical Biology、Journal of Theoretical Biology、Mathematical Biosciences、SIAM Journal on Matrix Analysis and- Applications等发表论文100余篇，指导博士后、博士生及国际访问学者20余人，论文被国际同行引用2000多次。