Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 162, pp. 1-17.
Asymptotic behavior of stochastic Gilpin-Ayala mutualism model with jumps
Xinhong Zhang, Ke Wang
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.
Show me the PDF file (394 KB),
TEX file, and other files for this article.
 |
Xinhong Zhang
Department of Mathematics, Harbin Institute of Technology
Weihai 264209, China
email: zhxinhong@163.com
|
 |
Ke Wang
Department of Mathematics, Harbin Institute of Technology
Weihai 264209, China
email: wangke@hitwh.edu.cn, Tel:+86 06315687086
|
Return to the EJDE web page