Observation of induced subcritical bifurcation by near-resonant perturbations

Abstract

We present the first experimental evidence that near-resonant perturbations produce a destabilizing shift of a subcritical bifurcation. This is in direct contrast to supercritical bifurcations, where near-resonant perturbations always suppress the instability. Using a normal form analysis we derive a generic scaling law relating the magnitude of the destabilizing shift \ensuremath{\mu} to the perturbation amplitude \ensuremath{\varepsilon} and detuning frequency \ensuremath{\delta}. The predictions are in excellent agreement with our experiments. In the limit of very small \ensuremath{\delta} the shift obeys a pure scaling law, \ensuremath{\mu}\ensuremath{\propto}(\ensuremath{\varepsilon}${)}^{2/3}$.