Nonlinear Dynamics

, Volume 77, Issue 3, pp 807–817 | Cite as

Asymptotic properties of a stochastic Lotka–Volterra cooperative system with impulsive perturbations

Original Paper

Abstract

A stochastic Lotka–Volterra cooperative system with impulsive effects is proposed and concerned. The existence and uniqueness of the global positive solution are investigated. The \(p\)th moment and the asymptotic pathwise properties are estimated. Finally, sufficient conditions for extinction and stability in the mean are presented. Our results show that the impulse does not affect the properties if the impulsive perturbations are bounded. However, if the impulsive perturbations are unbounded, then some properties could be changed significantly.

Keywords

Stochastic perturbations Cooperative system Impulsive effects Extinction Stable in the mean 

Notes

Acknowledgments

The authors would like to thank the editor and referee for making the valuable suggestions to improve this paper. This research was partially supported by grants from the National Natural Science Foundation of PR China (Nos. 11171081, 11171056, 11101183, 11301207, 11301112) Project (HIT.NSRIF.2015103) by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology, and Natural Science Research Project of Ordinary Universities in Jiangsu Province (No. 13KJB110002).

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of Technology (Weihai)WeihaiPeople’s Republic of China
  2. 2.College of ScienceChina University of Petroleum (East China)QingdaoPeople’s Republic of China

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