Asymptotic behaviour of the stochastic Lotka-Volterra model. (English) Zbl 1048.92027

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.


92D25 Population dynamics (general)
34F05 Ordinary differential equations and systems with randomness
60J65 Brownian motion
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