报告题目：Overexploitation and relaxation oscillation occur in the Rosenzweig-MacArthur model

报告时间：2023年6月25日 15:00-17:00

报告地点：腾讯会议：396721072

报告摘要：In this paper, we study a Rosenzweig-MacArthur predator-prey system with a strong Allee effect, and take a predator functional response to the hyperbolic tangent form as trigonometric. We study both the local and global dynamics, and the possible bifurcation is determined according to the variation of the carrying capacity of the prey. An analytic expression is given to determine the criticality of Hopf bifurcation, and the resulting Hopf bifurcation is proved to be supercritical or subcritical. The normal form of Bogdanov-Takens bifurcation at the positive equilibrium is derived. The existence of heteroclinic orbit and Bautin (generalized Hopf) bifurcation are also proved. Biologically speaking, such a heteroclinic cycle always forms a boundary of the region in two-parameter space which indicates the breakdown of the system after the invasion of the predator, i.e., overexploitation occurs. Interestingly, there are heteroclinic relaxation oscillations cycles caused by the strong Allee effect, or the high per capita death rate or the small intrinsic growth rate. More precisely, the strong Allee effect and the trigonometric functional response could be responsible for the existence of heteroclinic cycle and the occurrence of relaxation oscillations, respectively. Further, numerical simulations are given to demonstrate the theoretical results which include the coexistence of limit cycles and heteroclinic cycles.

报告人： 徐衍聪，中国计量大学理学院教授，博士生导师，华东师范大学应用数学专业博士，浙江大学博士后，美国工业与应用数学学会会员，美国数学会会员，浙江省数理医学会理事，浙江省ZSMM生物医学数学专业委员会主任，曾入选浙江省优秀中青年骨干教师，杭州市优秀教师，校优秀中青年支持计划，校教学十佳，校十佳班主任等。先后访问美国布朗大学，德国不莱梅大学，日本京都大学，加拿大约克大学等高校。主持国家自然科学基金面上项目、天元基金、日本全球卓越中心（GCOE）项目，归国留学基金、博士后基金、浙江省自然科学基金等。主要从事动力系统分支理论及应用研究。