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Mathematical Problems in Engineering
Volume 2016, Article ID 3407463, 9 pages
Research Article

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

1Department of Mathematics, Qingdao University of Technology, Qingdao 266520, China
2Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China

Received 6 August 2016; Accepted 9 November 2016

Academic Editor: Ana Carpio

Copyright © 2016 Lijie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.