Influence of fear effect on a Holling type III prey-predator system with the prey refuge

The aim of the paper is to study the impact of anti-predator behavior caused by dread of predator species in a prey predator system with Holling III type functional response and prey shelters. Firstly, we analyze the dynamic behavior of the system, including the stability of the system and demonstrating the occurrence of Hopf bifurcation around the positive equilibrium point and the existence of limit cycle emerging through Hopf bifurcation. Secondly, through the study of the effect of fear and refuge, we discover that the increase of fear level can improve the stability of the system by eliminating periodic solutions and decrease the populations of predator species at the coexist equilibrium, but not cause the extinction of the predators, and prey refuge also plays very vital role in the persistence of the predators. Finally, the rationality of the results is verified by numerical simulation.