Competitive Lotka-Volterra population dynamics with jumps

Jianhai Bao, Xuerong Mao, George Yin, Chenggui Yuan

Research output: Contribution to journalArticle

174 Citations (Scopus)

Abstract

This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) We discuss the uniform boundedness of $p$th moment with $p>0$ and reveal the sample Lyapunov exponents; (c) Using a variation-of-constants formula for a class of SDEs with jumps, we provide explicit solution for 1-dimensional competitive Lotka-Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our $n$-dimensional model.
Original languageEnglish
Pages (from-to)6601-6616
Number of pages16
JournalNonlinear Analysis: Theory, Methods and Applications
Volume74
Issue number17
DOIs
Publication statusPublished - Dec 2011

Keywords

  • variation-of-constants formula
  • Lotka–Volterra model
  • jumps
  • stochastic boundedness
  • Lyapunov exponent
  • extinction

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