arXiv:0903.4523 Abstract | arXiv Analytics

arXiv:0903.4523 [math.DS]Abstract References Reviews Resources

Oscillations near separatrix for perturbed Duffing equation

Published 2009-03-26Version 1

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.

Comments: 17 pages, 4 figures

Categories: math.DS, math-ph, math.MP

Keywords: perturbed duffing equation, oscillations, periodic perturbation generates, complicated dynamics close, saddle points

Related articles: Most relevant | Search more

arXiv:2104.13350 [math.DS] (Published 2021-04-27)

Queues with Updating Information: Finding the Amplitude of Oscillations

Philip Doldo, Jamol Pender

arXiv:math/0509630 [math.DS] (Published 2005-09-27, updated 2006-12-22)

Topological pressure via saddle points

Katrin Gelfert, Christian Wolf

arXiv:1412.0738 [math.DS] (Published 2014-12-01)

Birth of discrete Lorenz attractors at the bifurcations of 3D maps with homoclinic tangencies to saddle points