The definition has been adopted by the random dynamical systems community especially in the study of stochastic bifurcations, random attractors, stochastic resonance
, random horseshoe and in modelling real life problems such as climate dynamics.
Ward and colleagues  described stochastic resonance
as "a nonlinear cooperative effect wherein the addition of a random process, or 'noise' to a weak signal, or stimulus results in improved detectability or enhanced information content in some response." The human body cannot foresee impending vibration movements during stochastic vibration and, therefore, is constantly challenged to adapt its neural and muscular reactions.
However, there exists another rhythmic pattern formation mechanism: stochastic resonance
Read, 2004: Stochastic resonance
in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization.
Ozer, "Enhancement of pacemaker induced stochastic resonance
by an autapse in a scale-free neuronal networks", Sci.
The phenomenon of stochastic resonance
(SR) characterized the cooperative effect between weak signal and noise in a nonlinear systems, which was originally perceived for explaining the periodicity of ice ages in early 1980s [1, 2].
In the last years, many methods for enhancing the diagnosis-relevant information of rotating machinery, such as digital filters [10, 11], wavelet transform [12-14], stochastic resonance
(SR) [15, 16], manifold learning [17, 18], and morphological analysis [19, 20], have been invented.
methods were also used to purify the noisy envelope signal and enhance the FCF for bearing fault diagnosis [3, 6-8].
Chien- Chih Chen et.al  have studied the stochastic resonance
in the periodically forced Rikitake dynamo.
: A Mathematical Approach in the Small Noise Limit
algorithm (SRA)  is established based on a counterintuitive phenomenon that the signal-to-noise ratio (S/N) of a weak signal can be amplified significantly in a nonlinear system by making the best of noise instead of filtering it .
For examples, the proper local noise power can increase the signal-to-noise ratio of a noisy bistable system and optimize the stochastic resonance
of coupled systems, such as small-world and scale-free neuronal networks.