Strong Influence of Small Fluctuations in Nonlinear Systems

Recent investigations showed that even weak noise acting upon a nonlinear dynamical system can have a pronounced effect on its behaviour resulting in the transitions to a new state and in qualitative change in the system's properties, e.g., the transformation of an unstable equilibrium state into a stable one, and vice versa, the occurrence of multistability, noise-induced transport (stochastic ratchets), so-called stochastic resonance, and so on. The phenomenon of noise-induced transport is closely allied to the well-known problem of fluctuational transitions from one stable state to another. The theory of such transitions and examples of the phenomena indicated are considered.