活动时间：2024-09-27 10:00
活动地点：腾讯会议 139-763-890
主讲人：衣凤岐
主讲人中文简介：
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。国家重点研发计划会评专家、长江学者奖励计划评审专家。在包括J. Nonlinear Science, SIAM J.Appl.Math, JDE, JDDE, Physica D等杂志上发表论文20余篇。
活动内容摘要：
In this talk, I will report our recent work on the dynamics of a reaction-diffusion SIRS epidemic model with the general saturated nonlinear incidence rates. Firstly, for the ODEs system, we analyze the existence and stability of the disease-free equilibrium solution, the endemic equilibrium solutions as well as the bifurcating periodic solution. Our results also suggest that the ODEs system has a Allee effect, i.e., one can expect either the coexistence of a stable disease-free equilibrium and a stable endemic equilibrium solution, or the coexistence of a stable disease-free equilibrium solution and a stable periodic solution. Secondly, for the PDEs system, we are capable of deriving the Turing instability criteria in terms of the diffusion rates for both the endemic equilibrium solutions and the Hopf bifurcating periodic solution. The onset of Turing instability manifests itself as the appearance of new spatiotemporal patterns.
主持人：牛磊