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Defining a stability boundary for three species competition models

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  • van der Hoff, Quay
  • Greeff, Johanna C.
  • Fay, Temple H.

Abstract

A periodic steady state is a familiar phenomenon in many areas of theoretical biology and provides a satisfying explanation for those animal communities in which populations are observed to oscillate in a reproducible periodic manner. In this paper we explore models of three competing species described by symmetric and asymmetric May–Leonard models, and specifically investigate criteria for the existence of periodic steady states for an adapted May–Leonard model:x˙=r(1−x−αy−βz)xy˙=(1−βx−y−αz)yz˙=(1−αx−βy−z)z.

Suggested Citation

  • van der Hoff, Quay & Greeff, Johanna C. & Fay, Temple H., 2009. "Defining a stability boundary for three species competition models," Ecological Modelling, Elsevier, vol. 220(20), pages 2640-2645.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:20:p:2640-2645
    DOI: 10.1016/j.ecolmodel.2009.07.027
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    References listed on IDEAS

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    1. Fay, Temple H. & Greeff, Johanna C., 2008. "A three species competition model as a decision support tool," Ecological Modelling, Elsevier, vol. 211(1), pages 142-152.
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