Dynamics of a plant-herbivore-predator system with plant-toxicity

Zhilan Feng, Zhipeng Qiu, Rongsong Liu, Donald L. DeAngelis

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


A system of ordinary differential equations is considered that models the interactions of two plant species populations, an herbivore population, and a predator population. We use a toxin-determined functional response to describe the interactions between plant species and herbivores and use a Holling Type II functional response to model the interactions between herbivores and predators. In order to study how the predators impact the succession of vegetation, we derive invasion conditions under which a plant species can invade into an environment in which another plant species is co-existing with a herbivore population with or without a predator population. These conditions provide threshold quantities for several parameters that may play a key role in the dynamics of the system. Numerical simulations are conducted to reinforce the analytical results. This model can be applied to a boreal ecosystem trophic chain to examine the possible cascading effects of predator-control actions when plant species differ in their levels of toxic defense.

Original languageEnglish (US)
Pages (from-to)190-204
Number of pages15
JournalMathematical Biosciences
Issue number2
StatePublished - Feb 2011


  • Boreal ecosystem
  • Plant toxicity
  • Plant-herbivore interactions
  • Stability conditions
  • Tritrophic chain

ASJC Scopus subject areas

  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics


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