Dynamics behavior of a predator-prey diffusion model incorporating hunting cooperation and predator-taxis

Abstract

In this paper, we consider a predator-prey diffusion model incorporating hunting cooperation and predator-taxis. Firstly, we establish the global existence of classical solution for the model in any spatial dimension. Secondly, we analyze the instability caused by predator-taxis, and we observed that negative predator-taxis play the key role in inducing stability changes. Finally, numerical simulations are employed to validate the obtained results. MCS: Primary 35A09, 35K59; Secondary 35Q92, 92D25.