Nonequilibrium Systems with Random Control Parameters

Abstract

Most of the lectures in this school have been concerned with general properties and specific applications of nonlinear equations for a set of relevant variables. These equations describe the cooperative behavior of nonequilibrium systems in the frame-work reviewed by Haken1. There are two levels of discussion of these equations, the deterministic and the stochastic level. At the first level one usually studies the existence of the different homogeneous stationary states and also the spatial and temporal stationary structures which correspond to the different values of the control parameters. At this level of description fluctuations are neglected. The inclusion of fluctuations in the stochastic description allows the study of additional dynamical properties such as the relative stability of stationary states, decay of unstable and metastable states, transitions between stationary states for a fixed value of the control parameters etc. At both levels of description it is generally assumed that the control parameters have well defined constant values. In this seminar a stochastic description of nonequilibrium systems is considered in the case in which a control parameter becomes a random function of time. This describes the external noise situation defined more precisely below.