On damping in the vicinity of critical points

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.