The Inclusion of Noise

Abstract

In the introduction we pointed out that noise plays a crucial role especially at instability points. Here we shall outline how to incorporate noise into the approach developed in the previous chapters. In synergetics we usually start from equations at a mezoscopic level, disregarding the microscopic motion, for instance of molecules or atoms. The equations of fluid dynamics may stand as an example for many others. Here we are dealing with certain macroscopic quantities such as densities, macroscopic velocities, etc. Similarly, in biological morphogenesis we disregard individual processes below the cell level, for instance metabolic processes. On the other hand, these microscopic processes cannot be completely neglected as they give rise to fluctuating driving forces in the equations for the state variables q of the system under consideration. We shall not derive these noise sources. This has to be done in the individual cases depending on the nature of noise, whether it is of quantum mechanical origin, or due to thermal fluctuations, or whether it is external noise, produced by the action of reservoirs to which a system is coupled. Here we wish rather to outline the general approach to deal with given noise sources. We shall elucidate our approach by explicit examples.