2022西安电子科技大学非线性分析、微分方程与动力系统报告

报告题目：Spatiotemporal patterns of a delayed-diffusive predator-prey system with fear effects

报告人：衣凤岐 教授大连理工大学

照片：

邀请人：白振国

报告时间：2022年11月18日（周五）上午10：00-11：30

腾讯会议ID：464-533-014

报告人简介：衣凤岐，教授、博士生导师。现任职于大连理工大学数学科学学院，主要从事微分方程与动力系统的研究，特别关注反应扩散系统的分支理论及其应用。2008年获哈尔滨工业大学基础数学专业博士学位。2010年博士学位论文获得全国优秀博士学位论文提名论文；2013年入选教育部新世纪优秀人才支持计划；2014年主持的科研项目获得黑龙江省科学技术奖二等奖；2020年，入选大连市地方级领军人才。主持国家自然科学基金项目等项目多项，在研国家自然科学基金面上项目一项。

报告摘要：In this talk, I will report our recent works on the dynamics of a delayed-diffusive predator-prey system with fear effects, where a benefit from the ani-predation response in addition to the cost is taken into account. As a first step toward mathematically rigorous understanding the underlying mechanism of the spatiotemporal pattern formations, we are interested in how the joint effects of time delay, the fear effect strength, the carrying capacity, as well as the diffusion rates could affect the complex spatiotemporal pattern formations of the system. In particular, Turing instability of the Hopf bifurcating periodic solutions are investigated in details. To that end, a general formula is derived to determine Turing instability of the Hopf bifurcating periodic solutions for general 2-component delayed-diffusive system. This extends our earlier general results for non-delayed diffusive system to its delayed-diffusive counterparts. Our general formula tends to be new and can be applied to a variety of 2-component delayed-diffusive system. This talk is based on the joint works with Qiannan Song.