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

1 Department of Mathematics
Department of Mathematics (Kongens Lyngby, Denmark)
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.
Document type :
Journal articles

https://hal.inria.fr/hal-00924098
Contributor : Mathieu Desroches <>
Submitted on : Monday, January 6, 2014 - 12:29:32 PM
Last modification on : Thursday, January 7, 2021 - 3:26:20 PM

### Identifiers

• HAL Id : hal-00924098, version 1

### Citation

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

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