Changes in the dynamical behavior of nonlinear systems induced by noise

Weak noise acting upon a nonlinear dynamical system call have far-reaching consequences. The fundamental underlying problem - that of large deviations of a nonlinear system away from a stable or metastable state, sometimes re sulting in a transition to a new stationary state, in response to weak addi tive or multiplicative noise - has long attracted the attention of physicis ts. This is partly because of its wide applicability, and partly because it bears on the origins of temporal irreversibility in physical processes. Du ring the last few years it has become apparent that, in a system far from t hermal equilibrium, even small noise can also result in qualitative change in the system's properties, e.g., the transformation of an unstable equilib rium state into a stable one, and vice versa, the occurrence of multistabil ity and multimodality, the appearance of a mean field, the excitation of no ise-induced oscillations, and noise-induced transport (stochastic ratchets) . A representative selection of such phenomena is discussed and analyzed, a nd recent progress made towards their understanding is reviewed. (C) 2000 E lsevier Science B.V. All rights reserved.