This book contains all invited contributions of an interdisciplinary workshop of the UNESCO working group on systems analysis of the European and North American region entitled "Stochastic Phenomena and Chaotic Behaviour in Complex Systems". The meeting was held at Hotel Winterthalerhof in Flattnitz, Karnten, Austria from June 6-10, 1983. This workshop brought together some 20 mathematicians, physicists, chemists, biologists, psychologists and economists from different European and American coun tries who share a common interest in the dynamics of complex systems and their ana lysis by mathematical techniques. The workshop in Flattnitz continued a series of meetings of the UNESCO working group on systems analysis which started in 1977 in Bucharest and was continued in Cambridge, U.K., 1981 and in Lyon, 1982. The title of the meeting was chosen in order to focus on one of the current problems of the analysis of dynamical systems. A deeper understanding of the vari ous sources of stochasticity is of primary importance for the interpretation of experimental observations. Chaotic dynamics plays a central role since it intro duces a stochastic element into deterministic systems.

This book, the first in a series on this subject, is the outcome of many years of efforts to give a new all-encompassing approach to complex systems in nature based on chaos theory. While maintaining a high level of rigor, the authors avoid an overly complicated mathematical apparatus, making the book accessible to a wider interdisciplinary readership.

These Proceedings contain invited lectures presented at the third Interna tional Conference on "Irreversible Processes and Dissipative Structures" in Kiihlungsborn (German Democratic Republic) in March, 1985. These con ferences, the first of which was held in Rostock in 1977 and the second in Berlin in 1982, are devoted to the study of irreversible processes far from thermal equilibrium and to the phenomena of selforganization. The meet ing in Kiihlungsborn brought together some 160 mathematicians, physicists, chemists and biologists from 10 countries, who are all interested in the inter disciplinary field of synergetics. The main topics of the conference were basic concepts of selforganization and evolution, such as entropy, instabilities, nucleation, dissipative struc tures, chaos and turbulence. The contributions cover methods from ther modynamics, the theory of dynamic systems, stochastic and statistic theory, the method of Green's functions, the fluctuation-dissipation theorem, etc. Several problems are studied in more detail, e.g., the kinetics of nucleation especially in finite systems, the dynamics of interfaces, reaction-diffusion sys tems, chemical and biochemical pattern formation and information process ing. Further, several contributions are devoted to the development of the concepts of chaos and turbulence. The editors hope that the contributions collected in this volume will pro vide some new information about the field of selforganization, which is in full development now.

This book addresses a large variety of models in mathematical and computational neuroscience. It is written for the experts as well as for graduate students wishing to enter this fascinating field of research. The author studies the behaviour of large neural networks composed of many neurons coupled by spike trains. An analysis of phase locking via sinusoidal couplings leading to various kinds of movement coordination is included.

This book is an often-requested reprint of two classic texts by H. Haken: "Synergetics. An Introduction" and "Advanced Synergetics". Synergetics, an interdisciplinary research program initiated by H. Haken in 1969, deals with the systematic and methodological approach to the rapidly growing field of complexity. Going well beyond qualitative analogies between complex systems in fields as diverse as physics, chemistry, biology, sociology and economics, Synergetics uses tools from theoretical physics and mathematics to construct an unifying framework within which quantitative descriptions of complex, self-organizing systems can be made. This may well explain the timelessness of H. Haken's original texts on this topic, which are now recognized as landmarks in the field of complex systems. They provide both the beginning graduate student and the seasoned researcher with solid knowledge of the basic concepts and mathematical tools. Moreover, they admirably convey the spirit of the pioneering work by the founder of Synergetics through the essential applications contained herein that have lost nothing of their paradigmatic character since they were conceived.

This book integrates the theories of complex self-organizing systems with the rich body of discourse and literature developed in what might be called ‘social theory of cities and urbanism’. It uses techniques from dynamical complexity and synergetics to successfully tackle open social science questions.