Dynamics of Synergetic Systems

This book contains the invited papers of an international symposium on Synergetics which was held at ZIF (Center for interdisciplinary research) at Bielefeld. Fed. Rep. of Germany. Sept. 24. -29 . • 1979. In keeping with our previous meetings. this one was truly interdisciplinary. Synergetic systems are those that can produce macroscopic spatial. temporal or functional structures in a self-organized way. I think that these proceedings draw a rather coherent picture of the present status of Synergetics, emphasizing this time theoretical aspects, although the proceedings contain also important con tributions from the experimental side. Synergetics has ties to many quite different disciplines as is clearly mirrored by the following articles. Out of the many ties I pick here only one example which is alluded to in the title of this book. Indeed, there is an important branch of mathematics called dynamic systems theory for which the problems of Synergetics might become an eldorado. While, undoubtedly, a good deal of dynamic systems had been motivated by mechanics, such as celestial and fluid dynamics, theory Synergetics provides us with a wealth of related problems of quite different fields, e. g. , lasers or chemical reaction processes. In order to become adequately applicable, in quite a number of realistic cases dynamic systems theory must be developed further. This is equally true for a number of other approaches.

Inhalt
I. Introduction.- Lines of Developments of Synergetics.- II. Equilibrium Phase Transitions.- Critical Phenomena: Past, Present and Future.- Critical Properties of Relativistic Bose Gases.- III. Nonequilibrium Phase Transitions.- Collective Effects in Rasers.- Nonequilibrium Phase Transition in Highly Excited Semiconductors.- Nonequilibrium Transitions Induced by External White and Coloured Noise.- IV. Spatio-temporal Organization of Chemical Processes.- Chemical Waves in the Oscillatory Zhabotinskii System. A Transition from Temporal to Spatio-temporal Organization.- Propagating Waves and Target Patterns in Chemical Systems.- On the Consistency of the Mathematical Models of Chemical Reactions.- The Critical Behavior of Nonequilibrium Transitions in Reacting Diffusing Systems.- V. Turbulence and Chaos.- Diffusion-Induced Chemical Turbulence.- Chaos and Turbulence.- VI. Self-organization of Biological Macvomolecules.- Self-organization of Biological Macromolecules and Evolutionary Stable Strategies.- A Mathematical Model of the Hypercycle.- VII. Dynamics of Multi-unit Systems.- Self-organization Phenomena in Multiple Unit Systems.- Synchronized and Differentiated Modes of Cellular Dynamics.- Dynamics of Cell-Mediated Immune Response.- VIII. Models of Psychological and Social Behavior.- Bifurcations in Cognitive Networks: A Paradigm of Self-organization via Desynchronization.- Dynamics of Interacting Groups in Society with Application to the Migration of Population.- IX. Mathematical Concepts and Methods.- Structural Instability in Systems Modelling.- Stationary and Time Dependent Solutions of Master Equations in Several Variables.- Poissonian Techniques for Chemical Master Equations.- Index of Contributors.