Oscillations near separatrix for perturbed Duffing equation

Details Oscillations near separatrix for perturbed Duffing equation Oscillations near separatrix for perturbed Duffing equation

2009-03-26

arxiv.org/abs/0903.4523v1

Mathematics

Dynamical Systems

17 pages, 4 figures

Scientific paper

A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution is defined by a separatrix map. This map is obtained for any order of the perturbation parameter. Properties of this map show an instability of a motion for the perturbed system.

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