Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise

A competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are esta...

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Main Authors: Huili Xiang, Zhuang Fang, Zuxiong Li, Zhijun Liu
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/389638
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author Huili Xiang
Zhuang Fang
Zuxiong Li
Zhijun Liu
author_facet Huili Xiang
Zhuang Fang
Zuxiong Li
Zhijun Liu
author_sort Huili Xiang
collection DOAJ
description A competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. An example together with its corresponding numerical simulations is presented to confirm our analytical results.
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institution Kabale University
issn 1026-0226
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language English
publishDate 2015-01-01
publisher Wiley
record_format Article
series Discrete Dynamics in Nature and Society
spelling doaj-art-71da2ad98e374320868d3770ce9be11b2025-08-20T03:33:42ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/389638389638Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental NoiseHuili Xiang0Zhuang Fang1Zuxiong Li2Zhijun Liu3Key Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaKey Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaKey Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaKey Laboratory of Biologic Resources Protection and Utilization of Hubei Province, Hubei University for Nationalities, Enshi, Hubei 445000, ChinaA competitive system subject to environmental noise is established. By using the theory of stochastic differential equations and Lyapunov function, sufficient conditions for the existence, uniqueness, stochastic boundedness, and global attraction of the positive solution of the above system are established, respectively. An example together with its corresponding numerical simulations is presented to confirm our analytical results.http://dx.doi.org/10.1155/2015/389638
spellingShingle Huili Xiang
Zhuang Fang
Zuxiong Li
Zhijun Liu
Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise
Discrete Dynamics in Nature and Society
title Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise
title_full Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise
title_fullStr Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise
title_full_unstemmed Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise
title_short Asymptotic Behavior of Positive Solutions of a Competitive System Subject to Environmental Noise
title_sort asymptotic behavior of positive solutions of a competitive system subject to environmental noise
url http://dx.doi.org/10.1155/2015/389638
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AT zhuangfang asymptoticbehaviorofpositivesolutionsofacompetitivesystemsubjecttoenvironmentalnoise
AT zuxiongli asymptoticbehaviorofpositivesolutionsofacompetitivesystemsubjecttoenvironmentalnoise
AT zhijunliu asymptoticbehaviorofpositivesolutionsofacompetitivesystemsubjecttoenvironmentalnoise