Period doubling cascades in a predator-prey model with a scavenger

Joseph P. Previte, Kathleen A. Hoffman

Research output: Contribution to journalReview articlepeer-review

24 Scopus citations

Abstract

The dynamics of the classic planar two-species Lotka-Volterra predator-prey model are well understood. We introduce a scavenger species that scavenges the predator and is also a predator of the common prey. For this model, we analytically prove that all trajectories are bounded in forward time, and numerically demonstrate persistent bounded paired cascades of period-doubling orbits over a wide range of parameter values. Standard analytical and numerical techniques are used in the analysis of this model, making it an ideal pedagogical tool. We include exercises and an open-ended project to promote mastery of these techniques.

Original languageEnglish (US)
Pages (from-to)523-546
Number of pages24
JournalSIAM Review
Volume55
Issue number3
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Mathematics
  • Applied Mathematics

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