Environmental noise impact on regularity and extinction of population systems with infinite delay

Fuke Wu, Gang George Yin

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)772 - 785
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - 2012
Externally publishedYes

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