| Article ID: | iaor20112154 |
| Volume: | 217 |
| Issue: | 10 |
| Start Page Number: | 4944 |
| End Page Number: | 4959 |
| Publication Date: | Jan 2011 |
| Journal: | Applied Mathematics and Computation |
| Authors: | Vasilova Maja, Jovanovic Miljana |
| Keywords: | competition, stochastic differential equations |
In this paper we study the stochastic Gilpin–Ayala competition model with an infinite delay. We verify that the environmental noise included in the model does not only provide a positive global solution (there is no explosion in a finite time), but this solution is also stochastically ultimately bounded. We obtain certain asymptotic results regarding a large time behavior.