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On a Stochastic Lotka-Volterra Competitive System with Distributed Delay and General Lévy Jumps

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  • Lijie Zhang
  • Chun Lu
  • Hui Liu

Abstract

This paper considers a stochastic competitive system with distributed delay and general Lévy jumps. Almost sufficient and necessary conditions for stability in time average and extinction of each population are established under some assumptions. And two facts are revealed: both stability in time average and extinction have closer relationships with the general Lévy jumps, firstly; and secondly, the distributed delay has no effect on the stability in time average and extinction of the stochastic system. Some simulation figures, which are obtained by the split-step -method to discretize the stochastic model, are introduced to support the analytical findings.

Suggested Citation

  • Lijie Zhang & Chun Lu & Hui Liu, 2016. "On a Stochastic Lotka-Volterra Competitive System with Distributed Delay and General Lévy Jumps," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-9, December.
    • Handle: RePEc:hin:jnlmpe:3407463
    DOI: 10.1155/2016/3407463
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