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报告题目：Degenerate Bogdanov-Takens bifurcation of codimension 4 in Holling-Tanner model with harvesting

报告人：黄继才教授

时间：2024年4月24日 9:30-11:30

地点：腾讯会议（会议号：489824690）

个人简介

黄继才，华中师范大学教授、博士生导师。2005年获中国科学院数学与系统科学研究院数学所博士学位。主要从事常微分方程定性理论、分岔理论及其应用研究。在 JDE、JDDE、P ROY SOC EDINB A、SIAP、SIADS、JMB、Chaos 等期刊发表学术论文六十余篇。

Abstract

In this talk, we revisit the Holling-Tanner model with constant-yield prey harvesting. It is shown that the highest codimension of a nilpotent cusp is 4, and the model can undergo degenerate Bogdanov-Takens bifurcation of codimension 4. Moreover, when the model has a center-type equilibrium, we show that it is a weak focus with order at least 3 and at most 4, and the model can exhibit Hopf bifurcation of codimension 3. Some algebraic methods including resultant elimination and pseudo-division are used to solve the semi-algebraic varieties of normal form coefficients or focal values. Our results indicate that constant-yield prey harvesting can cause not only richer dynamics and bifurcations, but also the coextinction of both populations with some positive initial densities.