Elsevier

Mathematical Biosciences

Volume 111, Issue 1, September 1992, Pages 73-87
Mathematical Biosciences

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

https://doi.org/10.1016/0025-5564(92)90079-CGet rights and content

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.

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    Research partially supported by the Natural Sciences and Engineering Research Council of Canada, Grant No. NSERC A 4823.

    ∗∗

    Research partially supported by a University of Alberta Ph.D. Scholarship.

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