报告题目：Complex dynamics of a predator-prey system with herd and schooling behavior: with or without delay and diffusion

报告人： 原三领 教授

报告时间：2021年5月22日（周六）16:30—18:00

报告地点：威廉希尔学术报告厅

报告摘要: In this paper, we propose and analyze a predator-prey system incorporating a new type functional response function accounting for both the herd behavior for prey and the schooling behavior for predator. In the absence of spatial diffusion and time delay, we prove the existence of extinction region and the stability of all feasible nonnegative equilibria. In addition, we obtain conditions under which the system undergoes saddlenode, Hopf and Bogdanov-Takens types of bifurcations. For the spatiotemporal system, we investigate the existence of Hopf bifurcation induced by time delay near one of the positive equilibria and derive conditions for determining the property of the bifurcating periodic solution by using the normal form theory and center manifold reduction. Further, we investigate the effects of time delay or/and diffusion on the dynamics of the system. Our numerical and theoretical results show that both time delay and spatial diffusion play significant roles in determining the dynamics of the system.

报告人简介: 原三领，上海理工大学教授，博士生导师，应用数学学科负责人，中国数学会生物数学学会常务理事，美国《Mathematical Reviews》评论员。研究方向为：微分方程与动力系统、生物数学。曾先后主持4项国家自然科学基金面上项目、3项上海市教委项目的研究工作。研究内容涉及微分方程与动力系统、种群动力学、流行病动力学、海洋生态学以及生物化学工程等诸多领域，具有多学科交叉的特点。曾多次受邀到国内和国际多所高校进行合作研究和学术交流。已在Journal of Differential Equations、Journal of Mathematical Biology、Journal of Theoretical Biology、Bulletin of Mathematical Biology等国内外重要学术刊物上发表SCI论文80余篇。

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