Oscillations near separatrix for perturbed Duffing equation
Dynamical Systems
2009-03-27 v1 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.0903.4523,
title = {Oscillations near separatrix for perturbed Duffing equation},
author = {O. M. Kiselev},
journal= {arXiv preprint arXiv:0903.4523},
year = {2009}
}
Comments
17 pages, 4 figures