报告题目：Existence of limit cycles and homoclinic bifurcation in a plant-herbivore model with toxin-determined functional response

报告时间：2016年12月15日上午9:00

报告地点：数学馆 310

报告人： 中山大学赵育林教授

报告摘要：In this talk we study a two-dimensional toxin-determined functional response model (TDFRM). The toxin-determined functional responseexplicitly takes into consideration the reduction in the consumption of plants by herbivore due to chemical defence, which generates more complex dynamics of the plant-herbivore interactions. The purpose of the present paper is to analyze the existence of limit cycles and bifurcations of the model. By applying the theories of rotated vector fields and the extended planar termination principle, we establish the conditions for the existence of limit cycles and homoclinic loop. It is shown that a limit cycle is generated in a supercritical Hopf bifurcation and terminated in a homoclinic bifurcation, as the parameters vary.

专家简介：

赵育林，中山大学数学学院教授，博士生导师。目前主要从事常微分方程定性理论和分支理论的研究工作，包括弱化的Hilbert 十六问题、周期单调性、代数极限环、高阶极限环分支问题等。 2001年以来主持国家自然科学基金三项、广东省自然科学基金两项、教育部留学回国人员启动基金一项。