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Effects of prey refuges on a predator-prey model with a class of functional responses: The role of refuges. (English) Zbl 1160.92043
Summary: The effects of refuges used by prey on a predator-prey interaction with a class of functional responses are studied by using an analytical approach. The refuges are considered as two types: a constant proportion of prey and a fixed number of prey using refuges. We 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 the 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 in disagreement with previous results in this field.

MSC:
92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
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