Competitive Lotka–Volterra population dynamics with jumps

Jianhai Bao, Xuerong Mao, Geroge Yin, Chenggui Yuan

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Abstract

This paper considers competitive Lotka–Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show that a stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) we discuss the uniform boundedness of the pth 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 an explicit solution for one-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

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

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