Journal article
Canards and mixed-mode oscillations in a forest pest model
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.
Language: | English |
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Year: | 2010 |
Pages: | 238-242 |
ISSN: | 10960325 and 00405809 |
Types: | Journal article |
DOI: | 10.1016/j.tpb.2010.02.003 |
ORCIDs: | Brøns, Morten |
Animals Ecosystem Models, Statistical Models, Theoretical Population Dynamics Trees