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Journal Articles Mathematical Population Studies Year : 2014

Mixed-mode oscillations due to a singular Hopf bifurcation in a forest pest model

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 very 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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Dates and versions

hal-00924098 , version 1 (06-01-2014)

Identifiers

  • HAL Id : hal-00924098 , version 1

Cite

Morten Brøns, Mathieu Desroches, Maciej Krupa. Mixed-mode oscillations due to a singular Hopf bifurcation in a forest pest model. Mathematical Population Studies, 2014, pp.1-22. ⟨hal-00924098⟩
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