Synergetics - Some Basic Concepts and Recent Results

Abstract

In my contribution I should like to give a brief outline of some basic ideas of synergetics [1], [2] Then I shall present some of our recent results obtained by an application of our mathematical methods. The word SYNERGETICS is composed of two greek words and means COOPERATION. What we study in this field is the cooperation of individual parts of a system so that a self-organized formation of spatial, temporal, or functional structures on macroscopic scales becomes possible. In particular we shall ask whether there are general principles which govern self-organization irrespective of the nature of the individual subsystems which may be electrons, molecules, photons, biological cells, or animals. Or, to use an idea expressed by Danilov and Kadomtsev [3], synergetics can be considered as a search for universal mathematical models (of self-organization). In particular, we wish to develop an operational approach in the sense of general systems theory. Such kind of approach has [Teen persued in the Soviet Union by Lyapunov, Mandelstam, Andronov, Vitt, Chaikin, and many others.