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2007, Volume 4, Issue 1: 29-46. Doi: 10.3934/mbe.2007.4.29
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The dynamics of a stoichiometric plant-herbivore model and its discrete analog

  • 1.

    School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, P. R.

  • 2.

    School of Mathematics and Statistics, and Key Laboratory for Vegetation Ecology of the Education Ministry, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024

  • 3.

    Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588

  • 4.

    Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804

Received:  June 2006
Revised:  July 2006
Published:  October 2006
Abstract Related Papers Cited by
    Abstract
  • Stoichiometry-based models brought into sharp focus the importance of the nutritional quality of plant for herbivore-plant dynamics. Plant quality can dramatically affect the growth rate of the herbivores and may even lead to its extinction. These results stem from models continuous in time, which raises the question of how robust they are to time discretization. Discrete time can be more appropriate for herbivores with non-overlapping generations, annual plants, and experimental data collected periodically. We analyze a continuous stoichiometric plant-herbivore model that is mechanistically formulated in [11]. We then introduce its discrete analog and compare the dynamics of the continuous and discrete models. This discrete model includes the discrete LKE model (Loladze, Kuang and Elser (2000)) as a limiting case.
    Mathematics Subject Classification: 92D40, 34K20.

    Citation:
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