MIDIT OFD CATS Modelling, Nonlinear Dynamics Optics and Fluid Dynamics Chaos and Turbulence Studies and Irreversible Thermodynamics Risø National Laboratory Niels Bohr Institute and Technical University of Denmark Building 128 Department of Chemistry Building 321 P.O. Box 49 University of Copenhagen DK-2800 Lyngby DK-4000 Roskilde DK-2100 Copenhagen Ø Denmark Denmark Denmark
by Professor Hermann Haken
Institute for Theoretical Physics I
Center of Synergetics
University of Stuttgart
Germany
Phone: +0049/711/685-4990/4991/4989
Fax: +0049/711/685-4909
e-mail: HAKEN@THEO.PHYSIK.UNI-STUTTGART.DE
Abstract: The interdisciplinary field of synergetics deals with complex systems that are composed of many individual parts that interact with each other in a more or less complicated fashion. Synergetics focuses its attention on those situations, where as a consequence of a change of external influences described by control parameters the state of a system changes qualitatively. The systems treated are open systems, i.e. systems driven by an influx of energy, matter and/or information. The systems are described by nonlinear partial stochastic differential or integral equations. Nevertheless the basic principles can be explained in simple terms, namely instability, order parameters, the slaving principle. As is shown, even complex systems can be reduced in their complexity when they change the macroscopic states qualitatively. The standard example of the laser as a synergetic system is recapitulated in order to illuminate the basic concepts. It is shown how these concepts can be used to understand brain functioning in view of more recent experimental findings both at the microscopic level of neurons and the macroscopic level of psychological and physiological behavior. I will also introduce the concept of the synergetic computer that allows for pattern recognition and represents a genuine alternative to neural networks. Its extension allows one to cope with assignment problems in manufacturing by a novel approach in terms of dynamic systems. I shall also elucidate the relationships with the theory of dissipative structures, bifurcation theory, dynamical systems theory, the centermanifold theory, stochastic approaches, catastrophy theory, etc. at a level that will be understandable to a wide audience.