An organizing center of codimension 4 in a predator-prey model: from asymptotic dynamics to transients.

讲座时间 Datetime: 2023年3月5日，星期天，16:00-17:30

地点 Venue: 海琴二号457

主持人 Host：赵育林 教授

报告人 Speaker: 黄继才  教授

单位 Affiliation: 华中师范大学

报告摘要 Abstract:

In this talk, we take Rosenzweig-MacArthur (RM) model with generalist predator as an example in a constant or changing environment. When the environment is fixed, we provide a more easily verifiable classification, in terms of the coefficients of the system with nilpotent linear part and general higher terms, to determine the types and   codimension of nilpotent singularities in a general planar system. Second, by using some algebraic methods, we show that the highest codimension of a nilpotent focus is 4 and the sample RM model with generalist predator can exhibit nilpotent focus bifurcation of codimension 4. When the environment is changing, we study the impact of the rate and intensity of a nonlinear environmental change on dynamics. It is based on a joint work with Min Lu and Professor Hao Wang.

报告人简介：

黄继才教授，现任华中师范大学教授博士生导师,黄继才教授分别于1999年、2002年本科、硕士毕业于华中师范大学数学系，2005年获得中国科学院数学与系统科学研究院数学所博士学位。现为华中师范大学教授、博士生导师。黄教授主要从事常微分方程定性理论、分支理论及其应用研究。在J. Differential Equations、SIAM J. Appl. Math.、SIAM J. Appl. Dyn. Syst.、Bull. Math. Biol.等期刊发表学术论文三十多篇，先后主持国家自然科学基金3项。