Impact of the fear effect in a prey-predator model incorporating a prey refuge

By Huisen Zhang, Yongli Cai, Shengmao Fu, Weiming Wang. Applied Mathematics and Computation, 2019

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Abstract 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.

Subfields: Genetics, Public Health, Environmental and Occupational Health, Sociology and Political Science

View Paper: https://www.semanticscholar.org/paper/c516562647c48e2f73437b523ce20fe6d6b669ee