A discrete prey-predator model preserving the dynamics of a structurally unstable Lotka-Volterra model

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Abstract

Leslie's method to construct a discrete two dimensional dynamical system dynamically consistent with the Lotka-Volterra type of competing two species ordinary differential equations is applied in a newly extended manner for the Lotka-Volterra prey-predator system which is structurally unstable. We show that, independently of the time step size, the derived discrete prey-predator system is dynamically consistent with the continuous counterpart, keeping the nature of neutrally stable periodic orbit. Further, we show that the extended method to construct the discrete prey-predator system can provide a dynamically consistent model also for the logistic Lotka-Volterra one.

Original languageEnglish
Pages (from-to)1155-1170
Number of pages16
JournalJournal of Difference Equations and Applications
Volume13
Issue number12
DOIs
Publication statusPublished - 2007 Dec

Keywords

  • Dynamically consistent
  • Lotka-Volterra system
  • Neutrally stable
  • Population dynamics
  • Prey-predator model

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Applied Mathematics

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