Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model |
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Authors: | Morten Brøns Mathieu Desroches |
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Institution: | 1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark;2. Inria Paris-Rocquencourt Research Centre, Domaine de Voluceau, Le Chesnay, France |
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Abstract: | In a forest pest model, young trees are distinguished from old trees. The pest feeds on old trees. The pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. A combination of a singular Hopf bifurcation and a “weak return” mechanism, characterized by a small change in one of the variables, determines the features of the mixed-mode oscillations. Period-doubling and saddle-node bifurcations lead to closed families (called isolas) of periodic solutions in a bifurcation corresponding to a singular Hopf bifurcation. |
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Keywords: | canards forest pest model mixed-mode oscillations singular Hopf bifurcation slow-fast systems |
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