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

H. I. Freedman, Shigui Ruan

Research output: Contribution to journalArticle

40 Citations (Scopus)

Abstract

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
Volume111
Issue number1
DOIs
StatePublished - 1992
Externally publishedYes

Fingerprint

Food Chain Model
Food Chain
Hopf bifurcation
Conservation of Natural Resources
bifurcation
food chain
Hopf Bifurcation
Bifurcation
Bifurcation (mathematics)
Carrying Capacity
Local Stability
Prey
carrying capacity
Unstable
Model
defence

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Hopf bifurcation in three-species food chain models with group defense. / Freedman, H. I.; Ruan, Shigui.

In: Mathematical Biosciences, Vol. 111, No. 1, 1992, p. 73-87.

Research output: Contribution to journalArticle

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