Asymptotic behaviour of the stochastic Lotka-Volterra model

Mao, Xuerong and Sabanis, Sotirios and Renshaw, Eric (2003) Asymptotic behaviour of the stochastic Lotka-Volterra model. Journal of Mathematical Analysis and Applications, 287 (1). pp. 141-156. ISSN 0022-247X (https://doi.org/10.1016/S0022-247X(03)00539-0)

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Abstract

This paper examines the asymptotic behaviour of the 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.

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