Visions of Synergetics

Abstract

Synergetics is an interdisciplinary field of research. It deals with open systems that are composed of many individual parts that interact with each other and that can form spatial, temporal, or functional structures by self-organization. The research goal of synergetics is three-fold: (1) Are there general principles of self-organization? (2) Are there analogies in the behavior of self-organizing systems? (3) Can new devices be constructed because of the results (1) and (2)? From a mathematical point of view, synergetics deals with nonlinear partial stochastic differential equations and studies their solutions close to those points where the solutions change their behavior qualitatively. As I will show in my article, synergetics in its present form is based on the concepts of stability and instability, control parameters, order parameters, and the slaving principle. The slaving principle allows one to compress the information that is necessary to describe complex systems into a few order parameters. This is possible if systems are close to their instability points. But it appears that the order parameter concept is also applicable to situations away from such instabilities. At the level of the order parameter equations, profound analogies between otherwise quite different systems become visible. This allows one to realize the same process (for instance dealing with information) on quite different material substrates. The order parameter concept and the slaving principle are explained and their extension to discrete noisy maps and to delay equations are mentioned. These results can be applied to pattern formation in fluids, lasers, semiconductors, plasmas, and other fields. A section is devoted to the analysis of spatio-temporal patterns in terms of order parameters and the slaving principle. It is shown how the concepts of synergetics can be utilized to devise a new type of computer for pattern recognition. In connection with preprocessing, it can recognize patterns that are shifted, scaled or rotated in space and that are deformed. It can recognize scenes and also facial expressions as well as movement patterns. The learning procedure is briefly outlined. Because of the analogy principle of synergetics, this computer allows for hardware realizations by means of semiconductors and lasers. Decision-making by humans or machines is interpreted by means of an analogy with pattern recognition. Further sections are devoted to recognition of dynamic processes and learning by machines. In this author's opinion, synergetics will find important applications in medicine, for instance in the analysis of MEG and EEG patterns, and in the development of devices with brain-like functions. Future tasks of synergetics will be the application of the order parameter concept and the slaving principle to the integration of specialized computers or computer algorithms, for instance for the recognition of faces, movement patterns, and so on, into a computer network for scene analysis and decision making. This will also hold for complicated production processes and so on. Generally speaking, the potentialities of synergetics are based on its self-organization principles.