Defining a stability boundary for three species competition models

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

Ecological Modelling, 2009, vol. 220, issue 20, 2640-2645

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.

Keywords: Competing species; Stability boundary; Periodic steady states; Eigenvalue analysis (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecomod:v:220:y:2009:i:20:p:2640-2645

DOI: 10.1016/j.ecolmodel.2009.07.027

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