Dynamics of prey-predator n-species models with density dependent diffusion

This paper is concerned with the n-species predator-prey models in a bounded domain in two cases, one of which involves n−1 cooperative preys and the other involves n−1 competitive preys. In these models, the diffusion coefficients may be density dependent, and the reaction functions include ratio-dependent terms. Some simple conditions are obtained to ensure the dynamical behaviors of the time-dependent solutions in relation to some positive solutions or quasi-solutions of the steady-state problems, which include the existence of these solutions. This dynamical behaviors lead to the coexistence and global attractors of the predator-prey systems. Some numerical simulations are given in the end.