The dynamics of a stoichiometric plant-herbivore model and its discrete analog

Guangyu Sui, Meng Fan, Irakli Loladze, Yang Kuang

Research output: Contribution to journalArticle

10 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)29-46
Number of pages18
JournalMathematical Biosciences and Engineering
Volume4
Issue number1
StatePublished - Jan 1 2007

Keywords

  • Bifurcation
  • Discrete model
  • Droop equation
  • Plant-herbivore interaction
  • Stoichiometry

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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