Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model

Morten Brøns, Mathieu Desroches, Martin Krupa

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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.
Original languageEnglish
JournalMathematical Population Studies
Volume22
Issue number2
Pages (from-to)71-79
ISSN0889-8480
DOIs
Publication statusPublished - 2015

Keywords

  • Canards
  • Forest pest model
  • Mixed-mode oscillations
  • Singular Hopf bifurcation
  • Slow-fast systems

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