Boundedness and global stability of the predator–prey model with prey-taxis and competition. (August 2022) - Mi, Yingyuan; Song, Cui; Wang, Zhicheng
Abstract: In this paper, we consider a reaction–diffusion system of the population dynamics of two predators and one prey with prey-taxis and competition. We prove the global existence and uniform boundedness of the positive classical solutions for the fully parabolic system over a bounded domain with Neumann boundary conditions. Furthermore, we establish the asymptotic behavior of solutions by constructing some appropriate Lyapunov functionals. Our results not only generalize the previously known one, but also present some new conclusions.