Impact of the fear effect in a prey-predator model incorporating a prey refuge - Zhang, Huisen; Cai, Yongli; Fu, Shengmao; Wang, Weiming (Applied mathematics and computation, 2019)
•A prey-predator model incorporating fear factor is developed.•A globally stable theorem of coexistence equilibrium is established.•The existences of Hopf bifurcation and limit cycle are shown.•The fear effect can not only reduce the population density of predator, but also stabilize the system by excluding the existence of periodic solutions. In this paper, we investigate the influence of anti-predator behaviour due to the fear of predators with a Holling-type-II prey-predator model incorporating a prey refuge. We first provide the existence and stability of equilibria of the model. Next, we give the existence of Hopf bifurcation and limit cycle. In addition, we study the impact of the fear effect on the model analytically and numerically, and find that the fear effect can not only reduce the population density of predator at the positive equilibrium, but also stabilize the system by excluding the existence of periodic solutions. Moreover, we also find that prey refuge has great impact on the persistence of the predator.