The role of the toxin effect in the predator-prey system with prey-taxis

Abstract

This paper concerns the population dynamics of a predator-prey model with the effect of prey toxicity, which describes the phenomena that the preys release their own toxins to predators as a defensive measure for survival. Compared with the classical predator-prey system, this system has stronger nonlinear coupling structure due to the inclusion of a prey toxicity. By delicate decoupling energy estimates, we prove that this system possesses a globally bounded classical solution in a smooth bounded domain $\Omega \subset R^N(N\ge 2)$ with homogeneous Neumann boundary conditions. Furthermore, we find a threshold to classify the global asymptotic stability of the prey-only steady state and the coexistence steady state by constructing suitable Lyapunov functions.