Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

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


Lecture series

by Professor Hermann Haken
Institute for Theoretical Physics I
Center of Synergetics
University of Stuttgart
Phone: +0049/711/685-4990/4991/4989
Fax: +0049/711/685-4909

at MIDIT, Department of Mathematical Modelling, The Technical University of Denmark, Building 305, Room 053.

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.