The Noisy Oscillator : Random Mass and Random Damping

TL;DR

This paper investigates a linear damped oscillator affected by two types of multiplicative noise, namely random mass and damping, analyzing energy flow, stability, and stochastic resonance phenomena.

Contribution

It introduces general formulas for moments and explores the effects of combined noise sources on stability and stochastic resonance in the oscillator.

Findings

Random noise sources influence energy influx and dissipation.

Stability conditions for mean and energy are derived.

Stochastic resonance is enhanced by combined noise effects.

Abstract

The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of energy to the oscillator and its dissipation to the surrounding environment. A random mass implies that the surrounding molecules not only collide with the oscillator but may also adhere to it, thereby changing its mass. We present general formulas for the first two moments and address the question of mean and energetic stabilities. The phenomenon of stochastic resonance, i.e. the expansion due to the noise of a system response to an external periodic signal, is considered for separate and joint action of two sources of noise and their characteristics.