Oscillatory-to-nonoscillatory transition due to external noise in a parametric oscillator

Abstract

A degenerate parametric oscillator which is driven by a random current additionally applied to a sinusoidal pumping current is found to exhibit a new type of oscillatory‐to‐nonoscillatory transition. This noise‐induced phase transition has a different kind of critical behavior from that observed in usual phase transitions, that is, near the threshold the variance of the fluctuating output current remains constant, however, the critical slowing‐down does occur. A stochastic equation for the parametric oscillation which includes a random force multiplied by the amplitude itself is derived and the experimental results are fully accounted for in terms of that equation.