On damping in the vicinity of critical points.


Journal Article

The effect of damping on the behaviour of oscillations in the vicinity of bifurcations of nonlinear dynamical systems is investigated. Here, our primary focus is single degree-of-freedom conservative systems to which a small linear viscous energy dissipation has been added. Oscillators with saddle-node, pitchfork and transcritical bifurcations are shown analytically to exhibit several interesting characteristics in the free decay response near a bifurcation. A simple mechanical oscillator with a transcritical bifurcation is used to experimentally verify the analytical results. A transcritical bifurcation was selected because it may be used to represent generic bifurcation behaviour. It is shown that the damping ratio can be used to predict a change in the stability with respect to changing system parameters.

Full Text

Duke Authors

Cited Authors

  • Virgin, LN; Wiebe, R

Published Date

  • June 2013

Published In

Volume / Issue

  • 371 / 1993

Start / End Page

  • 20120426 -

PubMed ID

  • 23690637

Pubmed Central ID

  • 23690637

Electronic International Standard Serial Number (EISSN)

  • 1471-2962

International Standard Serial Number (ISSN)

  • 1364-503X

Digital Object Identifier (DOI)

  • 10.1098/rsta.2012.0426


  • eng