活動時間：2024-09-27 10:00
活動地點：騰訊會議 139-763-890
主講人：衣鳳岐
主講人中文簡介：
衣鳳岐，大連理工大學數學科學學院教授、博士生導師。主要從事微分方程與動力系統的研究，特别關注反應擴散系統的分支理論及其應用。2008年獲哈爾濱工業大學基礎數學專業博士學位。2010年博士學位論文獲得全國優秀博士學位論文提名論文；2013年入選教育部新世紀優秀人才支持計劃；2014年主持的科研項目獲得黑龍江省科學技術獎二等獎。2020年入選大連市地方級領軍人才。主持國家自然科學基金面上項目3項。國家重點研發計劃會評專家、長江學者獎勵計劃評審專家。在包括J. Nonlinear Science, SIAM J.Appl.Math, JDE, JDDE, Physica D等雜志上發表論文20餘篇。
活動内容摘要：
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