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| Title:
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Canards and mixed-mode oscillations in a forest pest model |
| Type:
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Journal articleJournal article |
| Participant(s):
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Technical University of Denmark
Email:
Technical University of Denmark
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| Abstract:
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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. |
| Published:
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in journal: Theoretical Population Biology (ISSN: 0040-5809) (DOI: http://dx.doi.org/10.1016/j.tpb.2010.02.003), vol: 77, issue: 4, pages: 238-242, 2010 |
| DOI:
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