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Effects of prey refuges on a predator-prey model with a class of functional responses: The role of refuges |
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| Authors: | Zhihui Ma Wenlong Li Wenting Wang Zizhen Li |
| Affiliation: | a Key Laboratory of Arid and Grassland Agroecology of Ministry of Education, Lanzhou 730000, China b School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China c School of Pastoral Agriculture Science and Technology, Lanzhou University, Lanzhou 730020, China d School of Statistics, Lanzhou University of Finance and Economics, Lanzhou 730000, China |
| Abstract: | In this paper, the effects of refuges used by prey on a predator-prey interaction with a class of functional responses are studied by using the analytical approach. The refuges are considered as two types: a constant proportion of prey and a fixed number of prey using refuges. We will evaluate the effects with regard to the local stability of the interior equilibrium point, the values of the equilibrium density and the long-term dynamics of the interacting populations. The results show that the effects of refuges used by prey increase the equilibrium density of prey population while decrease that of predators. It is also proved that the effects of refuges can stabilize the interior equilibrium point of the considered model, and destabilize it under a very restricted set of conditions which is disagreement with previous results in this field. |
| Keywords: | Predator-prey system Functional response Prey refuge Stability Stabilizing effect Destabilizing effect |
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