Dynamics of the prey–predator model with variable coefficients and degenerate diffusion coefficients

The long-time behaviors are an important topic in the study of reaction diffusion equations. It is of interest to understand effects of variable coefficients and degenerate diffusion coefficients on the dynamical properties of reaction diffusion equations. In this paper, we shall use some new methods and techniques to prove that the degradation of the diffusion coefficient of the prey and variable coefficients satisfying the appropriate conditions will not affect dynamical properties of the reaction–diffusion prey–predator model.