Spreading Speeds And Traveling Waves Of An Integrodifference Predator-Prey System

In this paper,the following integrodifference predator-prey system is studiedWhen the predator invades the territory of the prey,the traveling waves for the system and the spreading speeds of the predator in the system are considered.Assume that the intrinsic growth function of the prey is nondecreasing.Firstly,by using the refined estimates about the equation of predator and applying the result about the single equation,the spreading speed c*of the predator is established,which indicates the predator spreads spatially at the speed of c*.Furthermore,the existence of nontrivial traveling waves which leaves from the equilibrium(1,0)is presented by Schauder fixed point theorem and upper and lower solutions method if c>c*.If the intrinsic growth function of the predator is nondecreasing and c?c*,then we obtain the existence of traveling waves which connects the equilibrium(1,0)with the co-existence equilibrium.It is shown that the predator invades successfully the habitat of the prey.Meanwhile,by passing to limit functions,the result of c = c*is given which is based on the asymptotic behavior of the traveling waves in the case of c>c*.With the aid of the classical theory of spreading speeds and the construction of auxiliary equation of the predator,the nonexistence of traveling waves which connects the equilibrium(1,0)with the co-existence equilibrium is confirmed if c<c*.The results demonstrate the minimal wave speed of non-trivial traveling waves is equal to the spreading speed of the predator.