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In this paper, we consider a predator-prey diffusion model incorporating hunting cooperation and predator-taxis. Firstly, we establish the global existence of a classical solution for the model in any spatial dimension. Secondly, we analyze the stability/instability caused by predator-taxis, and we observe that predator-taxis play a key role in inducing stability changes. Specifically, if the positive equilibrium is stable for the corresponding reaction-diffusion model, the attractive predator-taxis can further stabilize the system, while the repulsive predator-taxis may lead to a change in spatial stability, if the positive equilibrium is unstable for the corresponding reaction-diffusion model, the attractive predator-taxis makes the model remain unstable, while the repulsive predator-taxis has a stabilizing effect. Finally, numerical simulations are employed to validate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we carry out some research on a predator–prey system with maturation delay, a stage structure for generalist predators and a Holling type-II functional response, which has already been proposed. First, for the delayed model, we obtain the conditions for the occurrence of stability switches of the positive equilibrium and possible Hopf bifurcation values owing to the growth of the value of the delay by applying the geometric criterion. It should be pointed out that when we suppose that the characteristic equation has a pair of imaginary roots λ = ± i ω (ω > 0) , we just need to consider i ω (ω > 0) due to the symmetry, which alleviates the computation requirements. Next, we investigate the nature of Hopf bifurcation. Finally, we conduct numerical simulations to verify the correctness of our findings. [ABSTRACT FROM AUTHOR]