Global dynamics of a predator-prey model with prey-taxis and hunting cooperation

The mathematical analysis of spatiotemporal distributions in many species exhibiting different predation mechanisms has attracted considerable attention in biology and ecology. In this article, we investigated a prey-taxis model involving hunting cooperation, which has more strong coupling structures. Utilizing energy estimates and semigroup theory, the global boundness of its classical solution was established when the hunting cooperation is weak in two dimensions. By means of Lyapunov functionals, the global asymptotically stability of the non-negative constant steady-state solution for the discussed model was established under certain assumptions on parameters. These results enrich the related researches on the prey-taxis model with Lotka-Volterra functional response, which has been studied by Jin and Wang.