Spatially heterogeneous invasion of toxic plant mediated by herbivory

Zhilan Feng, Wenzhang Huang, Donald L. DeAngelis

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Toxic Plants
Herbivory
Invasion
herbivores
Reaction-diffusion Model
Toxicity
Functional Response
Traveling Wave Solutions
Equilibrium Point
Extinction
Converge
toxicity
Interaction
Growth
toxins
extinction
Model

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)

Cite this

Spatially heterogeneous invasion of toxic plant mediated by herbivory. / Feng, Zhilan; Huang, Wenzhang; DeAngelis, Donald L.

In: Mathematical Biosciences and Engineering, Vol. 10, No. 5-6, 01.10.2013, p. 1519-1538.

Research output: Contribution to journalArticle

Feng, Zhilan ; Huang, Wenzhang ; DeAngelis, Donald L. / Spatially heterogeneous invasion of toxic plant mediated by herbivory. In: Mathematical Biosciences and Engineering. 2013 ; Vol. 10, No. 5-6. pp. 1519-1538.
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