Bifurcation analysis of a plant-herbivore model with toxin-determined functional response

Rongsong Liu, Zhilan Feng, Huaiping Zhu, Donald L. DeAngelis

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


A system of ordinary differential equations is considered which models the plant-herbivore interactions mediated by a toxin-determined functional response. The new functional response is a modification of the traditional Holling Type II functional response by explicitly including a reduction in the consumption of plants by the herbivore due to chemical defenses. A detailed bifurcation analysis of the system reveals a rich array of possible behaviors including cyclical dynamics through Hopf bifurcations and homoclinic bifurcation. The results are obtained not only analytically but also confirmed and extended numerically.

Original languageEnglish (US)
Pages (from-to)442-467
Number of pages26
JournalJournal of Differential Equations
Issue number2
StatePublished - Jul 15 2008
Externally publishedYes


  • Homoclinic bifurcation
  • Limit cycle
  • Plant-herbivore model
  • Stability

ASJC Scopus subject areas

  • Analysis


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