The Effect Of Prey Taxis On The Stability In A Three-Species Predator-Prey Model

A predator-prey-reaction diffusion system describes the spatial interaction be-tween predator and prey.During the predation process,in addition to the random diffusion of predator and prey,the direction of the predator,s movement is affected by the population density of the prey,thus resulting in prey taxis.Therefore,a reaction-diffusion system with prey taxis can better reveal the behavioral process of predation.In this paper,we study a three species predator-prey-reaction diffusion system with prey taxis.For the small prey taxis sensitivity coefficient,in bounded domains of axbitraxy spatial dimension,the global existence and boundedness of solutions in system are investigated by the semigroup theory.Furthermore,the influence of prey taxis on the stability of the positive equilibria in reaction-diffusion systems is obtained by Routh-Hurwitz criterion.Finally,the conclusions are applied to some typical models and verified by numerical simulation using MATLAB.