title: On damping in the vicinity of critical points.
abstract: 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.
authors.affiliation: School of Engineering, Duke University, Durham, NC 27708, USA.
authors.forename: L N
authors.initials: LN
authors.lastname: Virgin
authors.forename: R
authors.initials: R
authors.lastname: Wiebe
keywords: bifurcations; buckling; damping; nonlinear oscillators