报告题目1: Propagation of monostable traveling fronts in discrete periodic media with delay
报 告人1: 吴事良 教授(西安电子科技大学)
报告时间1: 2022 年5月 19日(星期四)下午2:00-3:00
报告题目2: Complex dynamics of a stage-structured model with delays and diapause in tick growth
报 告人2: 舒洪英 教授(陕西师范大学)
报告时间2: 2022年5月19日(星期四)下午3:00-4:00
报告地点:腾讯会议ID:576850856
邀 请人:金海洋教授
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数学学院
2022年5月17日
报告摘要1: In this talk, we study the front propagation for a class of discrete periodic monostable equations with delay and nonlocal interaction. We first establish the existence of rightward and leftward spreading speeds and prove their coincidence with the minimal wave speeds of the pulsating traveling fronts in the right and left directions, respectively. The dependency of the speeds of propagation on the heterogeneity of the medium and the delay term is also investigated. We find that the periodicity of the medium increases the invasion speed, in comparison with a homogeneous medium; while the delay decreases the invasion speed. Further, we prove the asymptotic behavior and uniqueness of all noncritical pulsating traveling fronts. Finally, we show that all noncritical pulsating traveling fronts are globally exponentially stable, as long as the initial perturbations around them are uniformly bounded in a weight space.
报告人简介1:吴事良, 西安电子科技大学数学与统计学院教授,博士生导师。现为中国数学会理事和陕西省数学会常务理事。主要研究方向为微分方程、动力系统及应用。完成国家自然科学基金3项,目前在研国家自然科学基金面上项目和陕西省杰出青年基金项目各1项,获陕西省科学技术奖一等奖两项、二等奖一项(第一完成人),获陕西省优秀博士学位论文奖以及第十一届陕西青年科技奖;入选2017年陕西省高等学校杰出青年人才计划。在相关领域的知名期刊,如Trans. Amer. Math. Soc.、SIAM J. Math Anal.、J. Differential equations、Proc. Amer. Math. Soc.、Nonlinearity、J. Dynam. Differential Equations、J. Nonlinear Science等发表论文多篇。
报告摘要1:We consider a delay differential equation for tick population with diapause, derived from an age-structured population model, with two time lags due to normal and diapause mediated development. We derive threshold conditions for the global asymptotic stability of biologically important equilibria, and give a general geometric criterion for the appearance of Hopf bifurcations in the delay differential system with delay-dependent parameters. By choosing the normal development time delay as a bifurcation parameter, we analyze the stability switches of the positive equilibrium, and examine the onset and termination of Hopf bifurcations of periodic solutions from the positive equilibrium. Under some technical conditions, we show that global Hopf branches are bounded and connected by a pair of Hopf bifurcation values. This allows us to show that diapause can lead to the occurrence of multiple stability switches, coexistence of two stable limit cycles, among other rich dynamical behaviours.
报告人简介2:舒洪英,2010年获哈尔滨工业大学博士学位。2011年至2014年先后在加拿大多所大学任AARMS博士后研究员。2014年至2018年任职同济大学特聘研究员,博士生导师。2018年至今任陕西师范大学特聘教授,博士生导师。2016年获上海市浦江人才计划,2017年获陕西省百人计划。主持2项国家自然科学基金项目,1项上海市自然科学基金项目和1项加拿大科研基金项目。主要研究微分动力系统及生物数学方面的应用。已发表SCI收录论文30余篇,分别发表在J. Math. Pures Appl., Journal of Differential Equations, SIAM Journal of Applied Mathematics, Nonlinearity, Journal of Dynamics and Differential Equations, Journal of Mathematical Biology,Bulletin of Mathematical Biology等SCI期刊上。