M.H Rahmanidoust

The topic of mathematical physics was important in the pastcentury. Meanwhile, the present century is related to the mathematicalbiology, mathematical ecology, etc. Regarding the system predator-preyequations is the base of most population models, many researchers wouldlike to study in this area. In this paper, the permanency of a nonlinear fourspecies cyclic predator-prey system will be analyzed. Indeed, in this modeleach species is not only a predator but also a prey. Moreover, the sigmoidaltype functional response is assumed. By using the differential inequalitytheory, we find out some sufficient conditions for the permanency of thesaid system.

Predator-Prey System, Permanence, Sigmoidal Type, Functional Response