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Mixed-Mode Oscillations Due to a Singular Hopf Bifurcation in a Forest Pest Model
| Content Provider | Semantic Scholar |
|---|---|
| Author | Brøns, Morten Desroches, M. |
| Copyright Year | 2017 |
| Abstract | We consider the dynamics of a three-variable model for forest pest proposed by Rinaldi and Muratori (Theor. Popul. Biol. 41:26–43, 1990.) The model divides the tree population into young and old trees, as the pest mainly feeds on the old trees. This gives rise to a three timescale structure where the pest grows on a fast scale, the young trees on an intermediate scale, and the old trees on a slow scale. Canard explosions of limit cycles and existence of mixed mode oscillations have previously been identified in the model, and it has been proposed that the mixed mode oscillations are organized by a folded node singularity. We show that the model indeed has a folded node, but that this is not the key to understanding the mixed mode oscillations. Rather, a singular Hopf bifurcation is present which organizes a transition from a stable steady state to relaxation oscillations which is much more complicated than the folded node scenario. We find numerically period doublings and saddle-node bifurcations leading to isolas of periodic solutions in a bifurcation structure consistent with a singular Hopf bifurcation. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://orbit.dtu.dk/files/127277497/postprint_3_.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Acrokeratosis Verruciformis of Hopf Anatomic Node Anatomic bifurcation Bifurcation theory Hopf bifurcation Limit cycle Linear programming relaxation Numerical analysis Plague Singular Solutions Steady state Trees (plant) |
| Content Type | Text |
| Resource Type | Article |
