Stochastic Kolmogorov-type population dynamics with variable delay

Fuke Wu, Shigeng Hu

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1 Citation (Scopus)


In general, population systems are often subject to environmental noise. To examine whether the presence of such noise affects population systems significantly, we stochastically perturb the delay Kolmogorov-type system dot x(t)=diag(x1(t),, xn(t))f(x(t), x(t-(t))) into the stochastic delay differential equation dx(t)=diag(x1(t),, xn(t))[f(x(t), x(t-(t)))dt+g(x(t), x(t-(t)))dw(t)]. Under the traditional diagonal dominance condition, we study the existence and uniqueness of the global positive solution of this stochastic system, and its asymptotic-bound properties. 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)129 - 150
Number of pages22
JournalStochastic Models
Issue number1
Publication statusPublished - 2009
Externally publishedYes

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