Existence and uniqueness of global positive solutions to the stochastic functional Kolmogorov-type system

In general, any population systems are often subject to various environmental noise. To examine whether the presence of such noise affects these systems significantly, we examine a stochastic functional Kolmogorov-type population system with the general stochastic perturbation. In this paper, we show that the environmental noise may suppress the potential population explosion and guarantee global existence of positive solutions when the noise intensity is strongly dependent on the population size. However, when the noise intensity is weakly dependent on the population size, the stochastic population system behaves similarly to the corresponding deterministic system. To illustrate our idea clearly, we also discuss some stochastic Lotka-Volterra systems as special cases.