Nonequilibrium Transitions Induced by External Noise

Abstract

Typically, the usual description of far from equilibrium systems is based on a set of ordinary or partial differential equations

$${\partial _t}x = f\left( {x,\beta }\right)$$

((1))

giving the spatio-temporal evolution of some systemic internal variables x as a function of some parametric variables β. Traditionally in dealing with these equations one assumes that the environment contains no sources of randomness susceptible to transform some of the β’s into fluctuating quantities. The environment is static and all parameters are well defined numerical constants. In many complex experimental or natural situations however these ideally deterministic conditions are not realized and a non negligible amount of “external noise” is always present. Drastic qualitative changes in macroscopic properties may then be observed. Our objective here is to report on some noise induced transition phenomena which occur already in rather simple systems. To be concrete, we shall discuss the influence of external noise on a model system. We will show that as the intensity of fluctuations increases the deterministic stability properties become irrelevant to predict the behavior of the internal systemic variables: new transition phenomena become possible. We shall comment on the class of systems to which the model belongs. More details concerning the results discussed here can be found in a recent series of papers.(1), (2), (3), (4).