Global dynamics and pattern formation for predator-prey system with density-dependent motion.

In this paper, we concern with the predator-prey system with generalist predator and density-dependent prey-taxis in two-dimensional bounded domains. We derive the existence of classical solutions with uniform-in-time bound and global stability for steady states under suitable conditions through the Lyapunov functionals. In addition, by linear instability analysis and numerical simulations, we conclude that the prey density-dependent motility function can trigger the periodic pattern formation when it is monotone increasing.