Spatially heterogeneous invasion of toxic plant mediated by herbivory

Zhilan Feng, Wenzhang Huang, Donald L. DeAngelis

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

Spatially homogeneous (ODE) and reaction-diffusion models for plant-herbivore interactions with toxin-determined functional response are analyzed. The models include two plant species that have different levels of toxicity. The plant species with a higher level of toxicity is assumed to be less preferred by the herbivore and to have a relatively lower intrinsic growth rate than the less toxic plant species. Two of the equilibrium points of the system representing significant ecological interests are E1, in which only the less toxic plant is present, and E2, in which the more toxic plant and herbivore coexist while the less toxic plant has gone to extinction. Under certain conditions it is shown that, for the spatially homogeneous system all solutions will converge to the equilibrium E2, whereas for the reaction-diffusion model there exist traveling wave solutions connecting E1 and E2.

Original languageEnglish (US)
Pages (from-to)1519-1538
Number of pages20
JournalMathematical Biosciences and Engineering
Volume10
Issue number5-6
DOIs
StatePublished - Oct 1 2013

Keywords

  • Invasion of toxic plant
  • Plant-herbivor interactions
  • Reaction-diffusion systems
  • Spatially heterogeneous
  • Traveling waves

ASJC Scopus subject areas

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

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