报告题目：Spatiotemporal pattern formations and Turing instability analysis for two different reaction-diffusion population-toxicant models with toxicant-taxis and periodic coefficients  

主讲人：衣凤岐教授

时 间：2025年11月26日（周三）15：00

地 点：腾讯会议(641-865-493)

主办单位：理学院

主讲人简介：

衣凤岐，大连理工大学数学科学学院教授、博士生导师。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面上项目3项。在包括J. Nonlinear Science, SIAP, JDE, JDDE, Physica D等杂志上发表论文20余篇。

摘要:

This talk is to report our recent works on two temporally periodic reaction-diffusion population-toxicant systems with toxicant-taxis. We are concerned particularly with the existence, exact multiplicity, stability and Turing instability of the positive spatially homogeneous temporally periodic solutions. First of all, it is proved that under certain conditions, the ODEs systems of these two systems may exhibit either exactly one positive periodic solution (stable) or exactly two positive periodic solutions (one is stable, the other is unstable). Secondly, it is demonstrated that, in the absence of cross-diffusions, the passive diffusions can never alter the stability of the positive periodic solutions in both systems. However, if the SKT type cross-diffusions continue to come to play, then Turing instability of the positive periodic solutions can be observed, indicating that cross-diffusions are the driving force for Turing instability of the periodic solutions. It is also found that the dynamics of system with direct toxicant-taxis (resp., SKT type cross-diffusion) stands in great contrast to that of system with indirect toxicant-taxis (resp., Keller-Segel type cross-diffusion).  This suggests that different cross-diffusions as well as different toxicant-taxis tends to play different roles in patterning. This talk is based on a joint work with Xiaotong Wu.