报告时间：2025年5月15日下午16:00-18:00

 报告地点：北区4号教学楼102室

 报告题目：Effect of fear In a General Discrete Predator-prey Model

 报告摘要：This study investigates the dynamics of a discrete predator-prey model that incorporates the fear effect. We begin by integrating the influence of fear on prey into a general discrete predator-prey framework. Subsequently, we analyze the dynamical properties of the system, including the existence of fixed points, their local stability, and potential bifurcations, utilizing bifurcation theory and the center manifold theorem. Specifically, we derive sufficient conditions for the occurrence of a flip bifurcation and a Neimark-Sacker bifurcation at the positive fixed point, using the fear level as the bifurcation parameter. Additionally, we establish criteria for the stability of the resulting bifurcated periodic orbits and invariant curves. The theoretical results are supported by numerical simulations, which demonstrate that the fear effect enhances the stability of the predator-prey system within a specific parameter range.

 报告人简介：袁沅，1984年于武汉大学获得学士学位，1988年于中南大学获得硕士学位，2002年于加拿大西安大略大学获得博士学位。2002年于滑铁卢大学做短暂博士后研究，随后于2002年9月起受聘于加拿大纽芬兰纪念大学，现为该校数学与统计系终身正教授和博士生导师。主要研究方向包括非线性动力系统的稳定性及分支分析、时滞微分方程及其在神经网络和生物数学中的应用、微分方程的符号及数值计算方法。已在SIAM Journal of Applied Mathematics, Journal of Mathematical Biology, Journal of Mathematical Analysis and Applications, Journal of Differential Equations, Nonlinear Analysis: Real World Applications, SIAM Journal on Applied Dynamical Systems等主要应用数学及生物数学杂志发表论文六十多篇。研究一直受到加拿大国家自然科学与工程理事会的资助，研究成果深受同行好评及引用。