In this monograph, a statistical description of natural phenomena is used to develop an information processing system capable of modeling non-linear relationships between sensory data. The system, based on self-organized, optimal preservation of empirical information, applies these relationships for prediction and adaptive control. This monograph is written for students, scientists and engineers in academia and industry who are interested in experimental work related to the adaptive modeling of natural laws, the development of sensory-neural networks, intelligent control, synergetics and informatics. No specific knowledge of advanced mathematics is presupposed. Examples taken from physics, engineering, medicine and economics demonstrate the applicability of such intelligent systems.

Hermann Haken (born 1927) is one of the “fathers” of the quantum-mechanical laser theory, formulated between 1962 and 1966, in strong competition with American researchers. Later on, he created Synergetics, the science of cooperation in multicomponent systems. The book concentrates on the development of his scientific work during the first thirty-five years of his career. In 1970 he and his doctoral student Robert Graham were able to show that the laser is an example of a nonlinear system far from thermal equilibrium that shows a phase-transition like behavior. Subsequently, this insight opened the way for the formulation of Synergetics. Synergetics is able to explain, how very large systems show the phenomenon of self-organization that can be mathematically described by only very few order parameters. The results of Haken’s research were published in two seminal books Synergetics (1977) and Advanced Synergetics (1983). After the year 1985 Haken concentrated his research on the macroscopic foundation of Synergetics. This led him towards the application of synergetic principles in medicine, cognitive research and, finally, in psychology. A comprehensive bibliography of Hermann Haken’s publications (nearly 600 numbers) is included in the book.

Different physical models for the Snoek-type relaxation in ternary systems (Fe-C-Me) are analyzed from the viewpoint of a distance of interatomic interaction taken into account: For non-saturated from the viewpoint of overlapping of interatomic interaction in b.c.c. alloys the physically sufficient and optimal for the computer simulation is the short-range model, which takes into account the interatomic interaction and the average amount of substitutional atoms in the first coordination shell, only. For high alloyed b.c.c. systems (i.e. with the overlapped interatomic interaction) the carbon atom undergoes an interaction of a few substitutional atoms simultaneously. That leads to the appearance of one broadened Snoek peak. Activation energy of such a peak is summed from the "elastic" and "chemical" interatomic interactions. Experimental results for alloys with b.c.c. solid solution structure and its computer simulations allow to introduce the new criterion for the high alloy state of monophase steels: the high alloyed state corresponds to the situation when substitutional atoms can not be considered any longer as the isolated atoms. From the viewpoint of mechanical spectroscopy this situation corresponds to the appearance of one broadened IF Snoek-type peak instead of two peaks existed for the steels with lower substitutional atom concentration.

This book is an introduction to the dynamics of reaction-diffusion systems, with a focus on fronts and stationary spatial patterns. Emphasis is on systems that are non-standard in the sense that either the transport is not simply classical diffusion (Brownian motion) or the system is not homogeneous. A important feature is the derivation of the basic phenomenological equations from the mesoscopic system properties. Topics addressed include transport with inertia, described by persistent random walks and hyperbolic reaction-transport equations and transport by anomalous diffusion, in particular subdiffusion, where the mean square displacement grows sublinearly with time. In particular reaction-diffusion systems are studied where the medium is in turn either spatially inhomogeneous, compositionally heterogeneous or spatially discrete. Applications span a vast range of interdisciplinary fields and the systems considered can be as different as human or animal groups migrating under external influences, population ecology and evolution, complex chemical reactions, or networks of biological cells. Several chapters treat these applications in detail.

The contributions to this book cover a wide range of applications of Soft Computing to the chemical domain. The early roots of Soft Computing can be traced back to Lotfi Zadeh's work on soft data analysis [1] published in 1981. 'Soft Computing' itself became fully established about 10 years later, when the Berkeley Initiative in Soft Computing (SISC), an industrial liaison program, was put in place at the University of California - Berkeley. Soft Computing applications are characterized by their ability to: • approximate many different kinds of real-world systems; • tolerate imprecision, partial truth, and uncertainty; and • learn from their environment. Such characteristics commonly lead to a better ability to match reality than other approaches can provide, generating solutions of low cost, high robustness, and tractability. Zadeh has argued that soft computing provides a solid foundation for the conception, design, and application of intelligent systems employing its methodologies symbiotically rather than in isolation. There exists an implicit commitment to take advantage of the fusion of the various methodologies, since such a fusion can lead to combinations that may provide performance well beyond that offered by any single technique.

This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.

We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. 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. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

The electronic processing of information permits the construction of intelligent systems capable of carrying out a synergy of autonomous measurement, the modeling of natural laws, the control of processes, and the prediction or forecasting of a large variety of natural phenomena. In this monograph, a statistical description of natural phenomena is used to develop an information processing system capable of modeling non-linear relationships between sensory data. The system, based on self-organized, optimal preservation of empirical information, applies these relationships for prediction and adaptive control. This monograph is written for students, scientists and engineers in academia and industry who are interested in experimental work related to the adaptive modeling of natural laws, the development of sensory-neural networks, intelligent control, synergetics and informatics. No specific knowledge of advanced mathematics is presupposed. Examples taken from physics, engineering, medicine and economics demonstrate the applicability of such intelligent systems.

These proceedings are from The Fourth International Conference on Bridge Management that consolidated the best and, more importantly, up-to-date research conducted in the field of bridge management. Since the first conference in 1990 the scientific art of bridge management has advanced at an astonishing rate. There has been a change from a curative to a preventative approach to bridge management, promising an increased longevity for the next generation of bridges and reduced whole-life costs, and practical and economical solutions have been found for some recurring problems.