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

In general, population systems are often subject to environmental noise. This paper considers the stochastic functional Kolmogorov-type system d x ( t ) = diag ( x 1 ( t ) , … , x n ( t ) ) [ f ( x t ) d t + g ( x t ) d w ( t ) ] . Under the traditionally diagonally dominant condition, we study exis...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 364; no. 1; pp. 104 - 118
Main Authors: Wu, Fuke, Hu, Shigeng, Liu, Yue
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 01.04.2010
Elsevier
Subjects:
Exact sciences and technology
Kolmogorov-type system
Lotka–Volterra system
Mathematical analysis
Mathematics
Moment average in time
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Sciences and techniques of general use
Stochastic functional differential equations
Stochastically ultimate boundedness
Stochastically ultimate boundedness
Kolmogorov-type system
Stochastic functional differential equations
Moment average in time
Lotka–Volterra system
Existence condition
Asymptotic behavior
Lotka-Volterra system
Global solution
Stochastic system
Functional
Mathematical analysis
Positive solution
Asymptotic solution
Application
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:In general, population systems are often subject to environmental noise. This paper considers the stochastic functional Kolmogorov-type system d x ( t ) = diag ( x 1 ( t ) , … , x n ( t ) ) [ f ( x t ) d t + g ( x t ) d w ( 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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2009.10.072