Dynamical properties of discrete Lotka-Volterra equations

Denis Blackmore, Jerry Chen, John Perez, Michelle Savescu

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

A discrete version of the Lotka-Volterra differential equations for competing population species is analyzed in detail in much the same way as the discrete form of the logistic equation has been investigated as a source of bifurcation phenomena and chaotic dynamics. It is found that in addition to the logistic dynamics - ranging from very simple to manifestly chaotic regimes in terms of governing parameters - the discrete Lotka-Volterra equations exhibit their own brands of bifurcation and chaos that are essentially two-dimensional in nature. In particular, it is shown that the system exhibits "twisted horseshoe" dynamics associated with a strange invariant set for certain parameter ranges.

Original languageEnglish (US)
Pages (from-to)2553-2568
Number of pages16
JournalChaos, Solitons and Fractals
Volume12
Issue number13
DOIs
StatePublished - Oct 1 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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