Article ID Journal Published Year Pages File Type
4617182 Journal of Mathematical Analysis and Applications 2012 14 Pages PDF
Abstract

Populations of biological species are often subject to different types of environmental noises. These noises play crucial roles and have significant impact on the evolution and biodiversity. To understand the effects of different types of noises on the asymptotic properties of the populations, this paper reveals the influence of inherent net birth noise and the interaction noise among stochastically perturbed population systems. By considering systems with infinite delays, (1) this paper discovers that (a) the interaction noise may suppress the potential explosion and guarantee the existence of the global solution, which yields regularity of the stochastic system, and (b) the inherent net birth noise may lead to extinction of the populations; (2) this paper provides sufficient conditions that ensure the stochastic persistence, stochastic boundedness, and asymptotic polynomial growth of the population system; (3) this paper demonstrates that these asymptotic properties are completely determined by stochastic noises and are independent of other parameters.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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