Books in the Springer Series in Synergetics series

Complex systems are ubiquitous, and practically all branches of science ranging from physics through chemistry and biology to economics and sociology have to deal with them. In this book we wish to present concepts and methods for dealing with complex systems from a unifying point of view. Therefore it may be of inter- est to graduate students, professors and research workers who are concerned with theoretical work in the above-mentioned fields. The basic idea for our unified ap- proach sterns from that of synergetics. In order to find unifying principles we shall focus our attention on those situations where a complex system changes its macroscopic behavior qualitatively, or in other words, where it changes its macroscopic spatial, temporal or functional structure. Until now, the theory of synergetics has usually begun with a microscopic or mesoscopic description of a complex system. In this book we present an approach which starts out from macroscopic data. In particular we shall treat systems that acquire their new structure without specific interference from the outside; i. e. systems which are self-organizing. The vehicle we shall use is information. Since this word has several quite different meanings, all of which are important for our purpose, we shall discuss its various aspects. These range from Shannon information, from which all semantics has been exorcised, to the effects of information on receivers and the self-creation of meaning.

This book illustrates how modern mathematical wavelet transform techniques offer fresh insights into the complex behavior of neural systems at different levels: from the microscopic dynamics of individual cells to the macroscopic behavior of large neural networks.

The vulnerability of our civilization to earthquakes is rapidly growing, rais ing earthquakes to the ranks of major threats faced by humankind. - Fundamental understanding of the lithosphere gained in earthquake prediction research. In addition, the theory of optimal control is used to link earthquake prediction with earthquake preparedness.

This book is primarily concerned with the computational aspects of predictability of dynamical systems - in particular those where observation, modeling and computation are strongly interdependent.

The earlier theory - linear nonequilibrium ther modynamics - is in principle a simple special case of the new theory. The presentation of the linear and nonlinear theories is done within a common theoretical framework that is not subject to the linearity condition.

Integrating the concepts of classical and elementary particle interaction, this volume includes stripped-down model equations adaptable to numerous systems showing particle-like structures, making it a valuable source for researchers and graduate students.

Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation.

We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory.

This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory.

Concepts, methods and techniques of statistical physics in the study of correlated, as well as uncorrelated, phenomena are being applied ever increasingly in the natural sciences, biology and economics in an attempt to understand and model the large variability and risks of phenomena.

This classic text and reference collects the many formulae and methods that can be found in the scientific literature on stochastic methods. This fourth edition has been thoroughly updated and restructured, and features a large amount of entirely new material.

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology.