Positive solution and its asymptotic behaviour of stochastic functional Kolmogorov-type system

Fuke Wu, Shigeng Hu, Yue Li

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27 Citations (Scopus)


In general, population systems are often subject to environmental noise. This paper considers the stochastic functional Kolmogorov-type system dx(t) = diag(x(1)(t), ... , x(n)(t))[f(x(t))dt + g(x(t))dw(t)]. Under the traditionally diagonally dominant condition, we study existence and uniqueness of the global positive solution of this stochastic system, and its asymptotic bound properties and moment average boundedness in time. These properties are natural requirements from the biological point of view. As the special cases, we also discuss some stochastic Lotka-Volterra systems.
Original languageEnglish
Pages (from-to)104 - 118
Number of pages15
JournalJournal of Mathematical Analysis and Applications
Issue number1
Publication statusPublished - 2010
Externally publishedYes

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