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

报告时间: 2022年6月22日(星期三), 20:00-20:40

报告地点: 腾讯会议 846 210 770

内容摘要: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.

报告人简介:华中师范大学教授、博士生导师。1999年、2002年分别本科、硕士毕业于华中师范大学数学系，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、分支理论及其应用研究。在 JDE、SIAP、SIADS、JDDE、JMB、BMB 等期刊发表学术论文四十余篇。其中发表在 SIADS (2019) 的文章被选为封面亮点文章, 并被美国工业与应用数学学会网站《SIAM News》专文报道。主持国家自然科学基金4项。曾获湖北省自然科学奖三等奖。

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数学与系统科学学院