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

Morten Brøns, Mathieu Desroches and Martin Krupa

Mathematical Population Studies, 2015, vol. 22, issue 2, 71-79

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.

Date: 2015
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DOI: 10.1080/08898480.2014.925344

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