Modeling And Analysis Of Age-Structured Population In A Spatiote-Mporal Periodic Environment

In the process of studying population growth,seasonal changes provide a dynamic environment for species.In order to understand the impact of seasonal changes on population dynamics,it is more practical to study the non-autonomous reaction-diffusion model.Based on the determination of the law of diffusion,a non-autonomous reactiondiffusion equation with time delay is proposed in this paper.Under appropriate ecological assumptions,the model is simplified,and three differential equation models of adult individuals with periodic delay on periodic lattices are established.In particular,the equation is not only periodic in the time environment,but also periodic in the spatial environment.Then,the basic reproduction ratio theory and global dynamics of one of the subsystems are studied,and define the basic reproduction ratio is the spectral radius of a next generation operator.Furthermore,on a suitably phase space,a threshold type result on the global dynamics are obtained by studying a semiflow: zero is globally asymptotically stable when the reproduction ratio is less than one,or stabilize at a periodic solution when the reproduction rate is greater than one.Finally,numerical simulations show the effects of different diffusion rates and time delays on population size.