Asymptotic Properties of Stochastic Functional Kolmogorov-Type System

作者：Wu, Fuke^*; Hu, Yangzi

来源：Acta Applicandae Mathematicae, 2009, 106(2): 251-263.

DOI：10.1007/s10440-008-9293-4

• Stochastic functional differential equations
• Kolmogorov-type system
• Lotka-Volterra system
• Global solution
• Asymptotic boundedness

In general, population systems are often subject to environmental noise. To examine whether the presence of such noise affects population systems significantly, this paper stochastically perturbs the functional Kolmogorov-type system.
(x) over dot(t) = diag(x(1)(t), ... , x(n)(t)) f(x(t))
into the stochastic functional differential equation
dx(t) = diag(x(1)(t), ... , x(n)(t))[f(x(t))dt + g(x(t))dw(t)].
This paper studies existence and uniqueness of the global positive solution of this stochastic system, its asymptotic boundedness and gives asymptotic pathwise estimation. These properties are natural requirements from the biological point of view.

• 出版日期2009-5
• 单位华中科技大学