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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.
MSC:
92D25Population dynamics (general)
34F05ODE with randomness
60J65Brownian motion