数学与统计学院学术报告预告

报告题目：Stability and bifurcation in a Leslie-Gowerpredator-prey model with Allee effect

报告人： 陈玉明 教授

报告时间：2022年10月22日9:00-11:00

报告地点：腾讯会议  ID：911-657-069

报告摘要：We consider a Leslie-Gower predator-prey model with Allee effect on the prey and a linearfunctional response. Here the Allee effect impacts the birth rate of the prey, which is differentfrom the common multiplicative and additive Allee effects. The model is well-posed, that is, allsolutions are bounded. Though the origin is not an equilibrium of the system, we prove thatit is an attractor by applying the blow-up method. The results on the existence and stabilityof equilibria indicate that the system undergoes bifurcations. With the help of Sotomayor’stheorem, we show the occurrence of saddle-node bifurcation. Moreover, there is degenerate Hopfbifurcation of codimension at least three. By choosing two (three) parameters of the system asbifurcation parameters and calculating a versal unfolding near the cusp, we demonstrate that thesystem undergoes Bogdanov-Takens bifurcation of codimension two (three). These theoreticalresults are supported with numerical simulations.

报告人简介：陈玉明，分别于1991年和1994年从北京大学获应用数学学士学位和硕士学位，并于2000年从加拿大约克大学（York University）获理学博士学位，2000年9月至2001年6月在加拿大阿尔伯塔大学（University of Alberta）做博士后。从2001年7月起，一直任教于加拿大罗瑞尔大学(Wilfrid Laurier University)。现为该校数学系教授、博士生导师。主要研究兴趣为动力系统和泛函微分方程理论及其在生物数学和神经网络中的应用。已在包括SIAM Journal on Mathematical Analysis，Transactions on the American Mathematical Society，Nonlinearity, Journal of Differential Equations，Physica D，Proceedings of the American Mathematical Society，Mathematical Biosciences，Neural Networks等国际著名刊物发表论文一百五十余篇，其成果被同行广泛引用，曾获安大略省科技与创新部早期研究者奖。先后主持5项加拿大国家自然科学与工程理事会(NSERC)科研基金项目，参与3项中国国家自然科学基金面上项目。