学术报告一

报告题目：Complex dynamics in a delay differential equation with two delays in tick growth with diapause

报告人：舒洪英 教授(陕西师范大学)

负责人：黄启华

报告时间：2024年1月12日（周五）下午15:00-16:00

报告地点：西南大学数学楼912学术报告厅

报告人简介：

舒洪英，2010年获哈尔滨工业大学博士学位。2008年在加拿大阿尔伯塔大学留学两年，2011年至2014年先后在加拿大新不伦瑞克大学、加拿大瑞尔森大学和约克大学任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3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其在生物数学上的应用，发表SCI收录论文40余篇，分别发表在J. Math. Pures Appl., SIAM Journal of Applied Mathematics, Journal of Differential Equations, Nonlinearity, Journal of Dynamics and Differential Equations, Journal of Mathematical Biology，Bulletin of Mathematical Biology 和Journal of Theoretical Biology等SCI期刊上。

报告摘要：

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 behaviors.

学术报告二

报告题目：Spatiotemporal patterns of a structured spruce budworm diffusive model

报告人：Xiangsheng Wang(汪翔升) 教授 (美国 University of Louisiana at Lafayette)

负责人：黄启华

报告时间：2024年1月12日（周五）下午16:00-17:00

报告地点：西南大学数学楼912学术报告厅

报告人简介：

汪翔升, 美国 University of Louisiana at Lafayette 大学副教授。毕业于香港城市大学和中国科学技术大学联合高等研究中心。他的研究兴趣包括渐近分析和生物数学等交叉学术领域，在Adv. Math., J. Differential Equations, J. Math. Biol., J. Math. Pures. Appl., SIAM J. Control Optim.等杂志上发表论文六十余篇。

报告摘要：

We formulate and analyze a general reaction-diffusion equation with delay, inspired by age-structured spruce budworm population dynamics with spatial diffusion by matured individuals. The model has its particular feature for bistability due to the incorporation of a nonlinear birth function (Ricker function) and a Holling type function of predation by birds. Here we establish some results about the global dynamics, in particular, the stability of and global Hopf bifurcation from the spatially homogeneous steady state when the maturation delay is taken as a bifurcation parameter. We also use a degree theoretical argument to identify intervals for the diffusion rate when the model system has a spatially heterogeneous steady state. Numerical experiments presented show interesting spatialtemporal patterns.