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Zbl 1143.34033
Li, Yanqiu; Gao, Hailong
Existence, uniqueness and global asymptotic stability of positive solutions of a predator-prey system with Holling II functional response with random perturbation. (English)
[J] Nonlinear Anal., Theory Methods Appl. 68, No. 6, A, 1694-1705 (2008). ISSN 0362-546X

Noting that environmental noise may well suppress a potential population explosion, the authors consider a randomized predator-prey system with Holling II functional response. It is shown that the positive solution of the associated stochastic delay differential equation does not explode to infinity in a finite time. Existence, uniqueness and global asymptotic stability of such solutions are also studied.
[Andrew Dale (Durban)]

MSC 2000:: *34F05 ODE with randomness
34D23 Global stability
92D25 Population dynamics

Keywords: randomized predator-prey system; Ito's formula; global stability

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