报告题目: Spatiotemporal Dynamics of a Structured Single Population Model
报告人: 舒洪英 陕西师范大学（Shanxi Normal University）
时间：12月13日（星期五），10:30-11:30
腾讯会议，会议号：305-589-030 密码：898989
摘要： First, 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. Secondly, 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. 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. Finally, we investigate the existence and stability of periodic solutions of switching dynamical systems consisting of two sub-equations, and develop general theorems to count the number of periodic solutions and find the basins of attractions for the periodic solutions and the trivial solution, respectively.
