Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 162, pp. 1-17.

Title: Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps
        
Authors: Xinhong Zhang (Harbin Institute of Technology, Weihai, China)
         Ke Wang       (Harbin Institute of Technology, Weihai, China)

Abstract:
 This article concerns the study of stochastic Gilpin-Ayala 
 mutualism models with white noise and Poisson jumps. Firstly, 
 an explicit solution for one-dimensional Gilpin-Ayala mutualism model 
 with jumps is obtained  and the asymptotic pathwise behavior is analyzed. 
 Then, sufficient  conditions for the existence of global positive solutions,
 stochastically  ultimate boundedness and stochastic permanence are 
 established for  the n-dimensional model. Asymptotic pathwise behavior 
 of n-dimensional  Gilpin-Ayala mutualism model with jumps is also discussed.
 Finally numerical examples are introduced to illustrate the results developed.

Submitted  May 17, 2013. Published July 19, 2013.
Math Subject Classifications: 34F05, 92D25, 60H10, 60H20.
Key Words: Gilpin-Ayala mutualism model; jumps; moment boundedness;
           asymptotic behavior; stochastic permanence.