Asymptotic behaviour of the stochastic Lotka-Volterra model

Xuerong Mao, Sotirios Sabanis, Eric Renshaw

Research output: Contribution to journalArticle

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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.

Original languageEnglish
Pages (from-to)141-156
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume287
Issue number1
DOIs
Publication statusPublished - 1 Nov 2003

Keywords

  • asymptotic behaviour
  • Brownian motion
  • Lotka-Volterra model
  • moment boundedness
  • stochastic differential equation

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