Hopf bifurcation in three-species food chain models with group defense

H. I. Freedman, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


Three-species food-chain models, in which the prey population exhibits group defense, are considered. Using the carrying capacity of the environment as the bifurcation parameter, it is shown that the model without delay undergoes a sequence of Hopf bifurcations. In the model with delay it is shown that using a delay as a bifurcation parameter, a Hopf bifurcation can also occur in this case. These occurrences may be interpreted as showing that a region of local stability (survival) may exist even though the positive steady states are unstable. A computer code BIFDD is used to determine the stability of the bifurcation solutions of a delay model.

Original languageEnglish (US)
Pages (from-to)73-87
Number of pages15
JournalMathematical Biosciences
Issue number1
StatePublished - Sep 1992
Externally publishedYes

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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