Spatial Dynamics Of Diffusive Predator-Prey Systems With Stage Structure

Population dynamics is an important subject in mathematical bio1ogy.Re-cently,there have been increasing attention and extensive investigations on non-local and time-delayed population models in order to study the effects of spatial diffusion and time delay on the evolutionary behavior of biological systems.It has become realized that the delay reaction diffusion equations can not well character-ize the spatial-temporal patterns.For example.consider a biological population. Since individuals are moving around.they have not been at the same point in space at preyious times.which results in the spatial nonlocality.As usual.for the population,there are two stages:immature stage and mature stage.Individuals that enters the mature stage at position χ will most likely have been born at some other point.y. For predator-prey,systems,predator takes time to convert prey biomass into predator biomass.which results in the spatial nonlocality.This thesis is mlainly concerned With uniform persistence,coexistence,and long-term behavior of non-local and delayed predator-prey system.We firstly obtain the model of growth of prey with immature and mature stage structure and a non-local delayed and diffusive predat,or model by integrating along chara,cteristics. We further study this predator-prey system from dynamical systems and semi-groups point of view.We show some condition on the persistence.coexistence. and ext inction of species.A threshold dynamics is established in t,erms of princi-pal eigenvalues for a nonlocal reaction-diffusion population model.Finally,using a fluctuation metl]od.We study the global attractiviti of the positive steady state for a interesting nonlocal and delayed reaction-diffusion system.