Properties of Solutions for Predator-prey Model with Prey-taxis and Additive Allee Effect
In order to study the effect of additive Allee effect on predator-prey model,and considering that the predator would always migrate to the place where the prey gathered,a predator-prey model with additive Allee effect and prey-taxis under homogeneous Neumann boundary conditions was established.Firstly,the comparison principle of elliptic equations was applied to obtain a priori estimates for the positive solution of the model.Secondly,the existence of the equilibria was given,and the stability of the equilibria was obtained by using the eigenvalue theory of linearization operators.Finally,regarding the chemotaxis coefficient as the bifurca-tion parameter,the local bifurcation solutions emanating from the normal constant solution were studied by using the Crandall-Rabi-nowitz local bifurcation theory.It was further proved that a transcritical bifurcation occured at this equilibrium point,thereby estab-lished the existence of non-constant positive solutions for the system.The results showed that the chemotaxis coefficient had an im-portant influence on the stability of coexistence solutions under the weak Allee effect.
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