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Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
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.
Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
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.
Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
Brøns, Morten (author) / Desroches, Mathieu / Krupa, Martin
2015
Article (Journal)
English
Local classification TIB:
770/1905/3175
BKL:
42.11
Biomathematik, Biokybernetik
/
74.80
Demographie
/
31.73
Mathematische Statistik
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