Food web chaos without subchain oscillators

Brian Bockelman, Bo Deng

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


A basic food web of four species is considered, of which there is a bottom prey X, two competing predators V, Z on X, and a super predator W only on Y. The main finding is that population chaos does not require the existence of oscillators in any subsystem of the web. This minimum population chaos is demonstrated by increasing the relative reproductive rate of Z alone without alternating any other parameter nor any nullcline of the system. It occurs as the result of a period-doubling cascade from a Hopf bifurcation point. The method of singular perturbation is used to determine the Hopf bifurcation involved as well as the parameter values.

Original languageEnglish (US)
Pages (from-to)3481-3492
Number of pages12
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number11
StatePublished - Nov 2005


  • Fast and slow dynamics
  • Food web
  • Holling type II form
  • Hopf bifurcation
  • Period-doubling to chaos
  • Predator and prey
  • Singular perturbation
  • Subchain oscillators
  • Super-predator

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics


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