Canards and mixed-mode oscillations in a forest pest model

Morten Brøns, Rune Kaasen

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    We consider a three-variable forest pest model, proposed by Rinaldi & Muratori (1992) [Rinaldi, S., Muratori, S., 1992. Limit cycles in slow-fast forest-pest models. Theor. Popul. Biol. 41,26-43]. The model allows relaxation oscillations where long pest-free periods are interspersed with outbreaks of high pest concentration. For small values of the timescale of the young trees, the model can be reduced to a two-dimensional model. By a geometrical analysis we identify a canard explosion in the reduced model, that is, a change over a narrow parameter interval from outbreak dynamics to small oscillations around an endemic state. For larger values of the timescale of the young trees the two-dimensional approximation breaks down, and a broader parameter interval with mixed-mode oscillations appear, replacing the simple canard explosion. The analysis only relies on simple and generic properties of the model, and is expected to be applicable in a larger class of multiple timescale dynamical models.
    Original languageEnglish
    JournalTheoretical Population Biology
    Volume77
    Issue number4
    Pages (from-to)238-242
    ISSN0040-5809
    DOIs
    Publication statusPublished - 2010

    Keywords

    • Mixed-mode oscillations
    • Forest pest
    • Canards

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