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Dynamical systems are often subject to random perturbations, and even for small perturbations, the resulting random dynamics can be drastically different from the deterministic one. For instance, in multistable systems arbitrarily small noise can enable transitions between stable states which would not be possible in the absence of noise. Whether such transitions are observed depends on the time scale of interest. The related concepts of phase transition, metastability and metastable time scales have been developed in the context of statistical-mechanics type models.

A different approach to random dynamical systems relies on concepts of stability and random attractors which are inspired by the analogous concepts for classical dynamical systems. The corresponding theory of bifurcations in random dynamical systems is still under development.