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 groovy mama ring derive the existence of classical solutions with uniform-in-time bound and global stability for steady states under suitable conditions through the tfh sarees with price 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.