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On Ebenman's model for the dynamics of a population with competing juveniles and adults

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Abstract

A general version of a model of Ebenman for the dynamics of a population consisting of competing juveniles and adults is analyzed using methods of bifurcation theory. A very general existence results is obtained for non-trivial equilibria and non-negative synchronous two-cycles that bifurcate simultaneously at the critical valuer=1 of the inherent net reproductive rater. Stability is studied in this general setting near the bifurcation point and conditions are derived that determine which of these two bifurcating branches is the stable branch. These general results are supplemented by numerical studies of the asymptotic dynamics over wider parameter ranges where various other bifurcations and stable attractors are found. The implications of these results are discussed with respect to the effects on stability that age class competition within a population can have and whether such competition is stabilizing or destabilizing.

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Author notes

  1. Jia Li

    Present address: Center for Nonlinear Studies, Theoretical Division, MS-B258, Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

Authors and Affiliations

  1. Department of Mathematics and Program on Applied Mathematics, University of Arizona, 85721, Tucson, AZ, USA

    J. M. Cushing & Jia Li

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  1. J. M. Cushing
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  2. Jia Li
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Supported by National Science Foundation Grant No. DMS-8714810.

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Cushing, J.M., Li, J. On Ebenman's model for the dynamics of a population with competing juveniles and adults. Bltn Mathcal Biology 51, 687–713 (1989). https://doi.org/10.1007/BF02459656

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  • DOI: https://doi.org/10.1007/BF02459656

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