Harmonic oscillator with fluctuating damping parameter.

The multiplicative noise in the equation of motion of an underdamped harmonic oscillator produced by a fluctuating damping parameter has a dramatic effect on the average coordinate of an oscillator. Noise of a sufficiently large strength leads to an instability. In the presence of an external periodic force, the output signal shows a nonmonotonic dependence on the strength and the rate of a color noise (stochastic resonance). Contrary to the case of a random frequency, this effect exists for white noise as well.