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Zbl 1048.92027
Mao, Xuerong; Sabanis, Sotirios; Renshaw, Eric
Asymptotic behaviour of the stochastic Lotka-Volterra model. (English)
[J] J. Math. Anal. Appl. 287, No. 1, 141-156 (2003). ISSN 0022-247X

Summary: This paper examines the asymptotic behaviour of a stochastic extension of a fundamentally important population process, namely the Lotka-Volterra model. The stochastic version of this process appears to have far more intriguing properties than its deterministic counterpart. Indeed, the fact that a potential deterministic population explosion can be prevented by the presence of even a tiny amount of environmental noise shows the high level of difference which exists between these two representations.

MSC 2000:: *92D25 Population dynamics
34F05 ODE with randomness
60J65 Brownian motion

Keywords: Lotka-Volterra model; Brownian motion; Moment boundedness; Asymptotic behaviour

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