# 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.
Type de document :
Article dans une revue
Mathematical Population Studies, Taylor & Francis (Routledge), 2014, pp.1-22

https://hal.inria.fr/hal-00924098
Contributeur : Mathieu Desroches <>
Soumis le : lundi 6 janvier 2014 - 12:29:32
Dernière modification le : vendredi 25 mai 2018 - 12:02:07

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• 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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