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Stochastic Gilpin-Ayala competition model with infinite delay. (English) Zbl 1206.92070
Summary: We study the stochastic M. E. Gilpin and F. J. Ayala [Proc. Natl. Acad. Sci. USA 70, 3590–3593 (1973; Zbl 0272.92016)] 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.
MSC:
92D40Ecology
34F05ODE with randomness
34K60Qualitative investigation and simulation of models
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