Abstract

We formulate a simple host–parasite type model to study the interaction of certain plants and herbivores. Our two-dimensional discrete-time model utilizes leaf and herbivore biomass as state variables. The parameter space consists of the growth rate of the host population and a parameter describing the damage inflicted by herbivores. We present insightful bifurcation diagrams in that parameter space. Bistability and a crisis of a strange attractor suggest two control strategies: reducing the population of the herbivore under some threshold or increasing the growth rate of the plant leaves.

Original languageEnglish (US)
Pages (from-to)89-101
Number of pages13
JournalJournal of biological dynamics
Volume2
Issue number2
DOIs
StatePublished - Apr 2008

Keywords

  • Bifurcation
  • Chaos
  • Control strategies
  • Host–parasite model
  • Plant–herbivore model

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

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