A reaction-diffusion equations modelling the effect of fluctuating water levels on prey-predator interactions

Prey-predator interactions are influenced by many ecological factors. In this paper, a prey-predator model with spatial diffusion under homogeneous Neumann boundary conditions is investigated to study the impact of water level on persistence of two fish populations living in an artificial lake. We obtain some important qualitative properties, including the existence of the global positive solution, the dissipation and permanence of this system. The existence of a unique globally stable periodic solution is also presented. Some numerical examples are presented to verify our results.