English

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.

Keywords

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

R2 v1 2026-06-21T12:44:43.342Z