Asymptotic behaviour of the stochastic Lotka-Volterra model

[摘要] 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. (C) 2003 Elsevier Inc. All rights reserved.

[发布日期] 2003-11-01

[关键词] Lotka-Volterra model;Brownian motion;stochastic differential equation;moment boundedness;asymptotic behaviour