Splitting of separatrices in the rapidly forced duffing oscillator

Research output: Chapter in Book/Report/Conference proceedingConference contribution


The splitting of the stable and unstable manifolds of the rapidly forced Duffmg oscillator with negative stiffness is investigated. The method used relies on the computation of analytic approximations for the orbits on the perturbed manifolds, and the asymptotic approximation of these orbits by successive integrations by parts. It is shown, that the splitting of the manifolds becomes exponentially small as the perturbation parameter tends to zero, and that the estimate for the splitting distance given by the Melnikov Integral dominates over high order corrections.

Original languageEnglish (US)
Title of host publication14th Biennial Conference on Mechanical Vibration and Noise
Subtitle of host publicationNonlinear Vibrations
PublisherAmerican Society of Mechanical Engineers (ASME)
Number of pages7
ISBN (Electronic)9780791811719
StatePublished - 1993
EventASME 1993 Design Technical Conferences, DETC 1993 - Albuquerque, United States
Duration: Sep 19 1993Sep 22 1993

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
VolumePart F167972-3


ConferenceASME 1993 Design Technical Conferences, DETC 1993
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation


Dive into the research topics of 'Splitting of separatrices in the rapidly forced duffing oscillator'. Together they form a unique fingerprint.

Cite this