SURVIVAL ANALYSIS OF A STOCHASTIC COOPERATION SYSTEM IN A POLLUTED ENVIRONMENT

Abstract

Stochastic cooperation model of two species with generalized dose-response function in a polluted environment is studied. Sufficient criteria for extinction, non-persistence in the mean, weak persistence in the mean, strong persistence in the mean and stochastic persistence are established. The threshold between weak persistence in the mean and extinction for each species is obtained. Certain long-run-average limits of the solutions are represented by two constants in some cases. The results also reveal that both the stochastic noises and the dose-response function play important roles in determining the persistence or extinction of the species.