Permanence of a discrete predator-prey system with nonmonotonic functional responses and endless delay

Abstract

A discrete-time analogue of predator-prey model with nonmonotonic functional responses and endless delay is considered in the paper. We investigate the question of obtaining conditions of permanent behavior of the dynamic model. The condition of permanence provides the limiting of the solutions but it requires the positiveness of the solutions. Sufficient conditions of permanence are obtained when the functional response function is nonmonotonic. The methods based on the estimation theorems are used to receive the sufficient permanent conditions of the solutions. These results are applied to some special population model with endless delay, some new results are obtained.