Dynamical Analysis Of Two Kinds Of Delayed Diffusive Predator-Prey Models

As one of the main research contents of biomathematics,population dynamics models have been widely used.Studying the relationship among species can predict population size,prevent alien species,protect rare animals,develop biological resources,and so on,which has important practical significance.The interaction between predator and prey is widespread in nature and affects ecological balance.Therefore,the predator-prey model has become a hot topic in population dynamics research.In this paper,two types of delayed diffusive predatorprey models are studied.Our purpose is to analyze the effects of delay,diffusion and nonlocal competition on the system.The main contents are as follows:1.A delayed predator-prey model with anti-predation behaviour is discussed.Assuming that additional food is provided for the predator population,the stability of the positive equilibrium are studied.Based on Hopf bifurcation theory,the existence of Hopf bifurcation is discussed.The properties of bifurcation are analyzed by using the theory of center manifold and normal form.Finally,the conclusions are verified by numerical simulations.The results show that delay can affect the stability of the system and induce Hopf bifurcation,diffusion can cause inhomogeneous periodic solutions and Turing instability.2.A predator-prey model with nonlocal competition and pregnancy delay is established.Selecting bifurcation parameter to study the local stability of the positive equilibrium and Hopf bifurcation.According to the theory of center manifold and normal form,some parameters which affect the properties of the bifurcation are derived.Then,numerical simulations are performed.It is found that the model exhibits spatial imhomogeneous periodic solutions.