Dynamics Research Of Several Kinds Of Prey-predator Model

Modeling predator–prey interactions and understanding the nonlinear dynamics of such interactions have been one of the most important and active topics in biological world and ecology.By means of the theory of delay differential equations,this paper study three kinds of prey-predator model.Firstly,a prey-predator model incorporating Allee effect and delay is constructed,and the influencing mechanism of Allee effect and delay on model is being analyzed.And then we track the direction of Hopf bifurcation and the stability of the periodic solutions by using center manifold theorem.The results indicate that Allee effect and delay play a key role in equilibrium state transition of model.Secondly,a prey-predator model is investigated in which the predator population is assumed to have an age structure.The critical conditions is derived for the occurrence of Hopf brand in the model by using integrated semigroup theory and Hopf bifurcation theory.The results imply that age play a key role in stability of the positive steady state of model.Finally,on the basis of the age-structured model that presented in Chapter III,The population diffusion is taken into account in the model.Using compression mapping principle and Schauder fixedpoint theorem,we prove the existence of periodic traveling wave solution and obtain the basic reproduction number and the minimum wave speed.The results show that the mature period and reproduction cycle play the important role in minimum wave speed.