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Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System

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  • Shengliang Guo
  • Zhijun Liu
  • Huili Xiang

Abstract

A stochastic competitive system is investigated. We first show that the positive solution of the above system does not explode to infinity in a finite time, and the existence and uniqueness of positive solution are discussed. Later, sufficient conditions for the stochastically ultimate boundedness of positive solution are derived. Also, with the help of Lyapunov function, sufficient conditions for the global attraction of positive solution are established. Finally, numerical simulations are presented to justify our theoretical results.

Suggested Citation

  • Shengliang Guo & Zhijun Liu & Huili Xiang, 2014. "Stochastically Ultimate Boundedness and Global Attraction of Positive Solution for a Stochastic Competitive System," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, September.
    • Handle: RePEc:hin:jnljam:963712
    DOI: 10.1155/2014/963712
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