 Canards and mixed-mode oscillations in a forest pest modelBrøns, Morten and Rune Kaasen Theoretical Population Biology, 2010, vol. 77, issue 4, 238-242 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. Keywords: Canards; Forest pest; Mixed-mode oscillations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:77:y:2010:i:4:p:238-242 DOI: 10.1016/j.tpb.2010.02.003 Access Statistics for this article Theoretical Population Biology is currently edited by Jeremy Van Cleve More articles in Theoretical Population Biology from Elsevier |
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