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This book deals with a series of topics on the cutting edge of nonlinear science, striking a balance between theory and experiment. It consists of two innovative introductory presentations on dynamical systems and fluid dynamics and six chapters on advanced research. A nontrivial interrelation between the different topics becomes apparent throughout the book as an indication of the underlying unity and genericity of nonlinear phenomena. There is a continuous emphasis on conceptual issues often i...

This volume consists of very high quality articles which not only give a very good account of this field in the Soviet Union, but also provide stimulating materials for researchers working on this topic.

This book is a collection of papers on the subject of nonlinear dynamics and its applications written by experts in this field. It offers the reader a sampling of exciting research areas in this fast-growing field. The topics covered include chaos, tools to analyze motions, fractal boundaries, dynamics of the Fitzhugh-Nagumo equation, structural control, separation of contaminations from signal of interest, parametric excitation, stochastic bifurcation, mode localization in repetitive structures...

Psychophysics is by definition mappings between events in the environment and levels of human sensory responses. In this text the methods of nonlinear dynamics, employing trajectories developed for simpler sensory modelling, are extended to classes of problems which lie at the interface between sensation and perception. A diversity of topics for which extensive empirical evidence exists are reformulated by writing their dynamics in terms of complex trajectories put into coupled lattices and into...

This text contains a survey of theories describing the evolution of random waves in nonlinear dispersive media. The three kinds of problems are considered. The first is the investigation of the evolution of initially random waves in nonlinear media describing the integrable and nearly integrable systems. It is important for many branches of acoustics and nonlinear optics, in particular for soliton transmissions in long optical communication systems. The second is the nonlinear waves propagation...

The basic procedures for designing and analysing electronic systems are based largely on the assumptions of linear behavior of the system. Nonlinearities inherent in all real applications very often cause unexpected and even strange behavior. This book presents an electronic engineer's perspective on chaos and complex behavior. It starts from basic mathematical notions which enable understanding of the observed phenomena, and guides the reader through the methodology and tools used in the labora...

A new vision of the most revolutionary scientific breakthrough of the twentieth century, and beyond.. In this fresh look at the science of complexity, a biologist and a computer scientist discuss this profound new field of knowledge, using examples from starfish to traveling salesmen, from car crashes to the workings of the brain. }Until recently, science has made progress by breaking large systems down into smaller and simpler parts, studying and explaining how these parts operate, and putting...

For engineering applications that are based on nonlinear phenomena, novel information processing systems require new methodologies and design principles. This perspective is the basis of the three cornerstones of this book: cellular neural networks, chaos and synchronization. Cellular neural networks and their universal machine implementations offer a well-established platform for processing spatial-temporal patterns and wave computing. Multi-scroll circuits are generalizations to the original C...

Although the mathematical theory of nonlinear waves and solitons has made great progress, its applications to concrete physical problems are rather poor, especially when compared with the classical theory of linear dispersive waves and nonlinear fluid motion. The Whitham method, which describes the combining action of the dispersive and nonlinear effects as modulations of periodic waves, is not widely used by applied mathematicians and physicists, though it provides a direct and natural way to t...

This is a reprint of M C Irwin's beautiful book, first published in 1980. The material covered continues to provide the basis for current research in the mathematics of dynamical systems. The book is essential reading for all who want to master this area.

The papers presented in this volume cover a number of different aspects of stochastic analysis, probability theory, quantum field theory, functional integration, ergodic theory, quantum theory, statistical modelling, random graph theory and percolation theory. The lectures also point out strong interactions between various fields: the fertility of the relations between probability theory and quantum theory and the intriguing and economical way of deriving the classical standard model by using no...

This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design proc...

Caustics are natural phenomena, forming light patterns in rainbows or through drinking glasses, and creating light networks at the bottom of swimming pools. Only in recent years have scientists started to artificially create simple caustics with laser light. However, these realizations have already contributed to progress in advanced imaging, lithography, and micro-manipulation. In this book, Alessandro Zannotti pioneers caustics in many ways, establishing the field of artificial caustic optic...

This book deals with the investigation of global attractors of nonlinear dynamical systems. The exposition proceeds from the simplest attractor of a single equilibrium to more complicated ones, i.e. to finite, denumerable and continuum equilibria sets; and further, to cycles, homoclinic and heteroclinic orbits; and finally, to strange attractors consisting of irregular unstable trajectories. On the complicated equilibria sets, the methods of Lyapunov stability theory are transferred. They are co...

This book presents leading-edge research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

The nature of this book is to emphasize the inherent complexity and richness of the human experience of change. Now, the author believes there to be an acceptable "scientific" explanation for this phenomona. Explored here are 30 years of studies to describe nonlinear dynamics, today termed either chaos theory or complexity theory. The connotations of both theories are discussed at length. Offering social scientists validation in their attempts to describe and define phenomona of a previously ine...

For the past two decades, ‘complexity’ has informed a range of work across the social sciences. There are diverse schools of complexity thinking, and authors have used these ideas in a multiplicity of ways, from health inequalities to the organization of large scale firms. Some understand complexity as emergence from the rule-based interactions of simple agents and explore it through agent-based modelling. Others argue against such ‘restricted complexity’ and for the development of case-based na...

"SCIENCE JOURNALISM AT ITS BEST. . . An impeccably researched, amazingly up-to-date, crisply written and well-illustrated survey." --Nature At the cutting edge of the sciences, a dynamic new concept is emerging: complexity. In this groundbreaking new book, Peter Coveney and Roger Highfield explore how complexity in mathematics, physics, biology, chemistry, and even the social sciences is transforming not only the way we think about the universe, but also the very assumptions that underlie conven...

John Holland is one of the few scientists, who all by themselves and by their pursuits, helped change the course of science and the wealth of human knowledge. There is hardly a field of science or problems, that is not affected by John's work on complexity and in particular, complex adaptive systems. On the occasion of his 85th birthday, many of his friends wrote about John, about facets of this remarkable man that only people close to him can know and tell.This book collects those stories highl...

The purpose of this volume is to give a detailed account of a series of re­ sults concerning some ergodic questions of quantum mechanics which have the past six years following the formulation of a generalized been addressed in Kolmogorov-Sinai entropy by A.Connes, H.Narnhofer and W.Thirring. Classical ergodicity and mixing are fully developed topics of mathematical physics dealing with the lowest levels in a hierarchy of increasingly random behaviours with the so-called Bernoulli systems at its...

Our life is a highly nonlinear process. It starts with birth and ends with death; in between there are a lot of ups and downs. Quite often, we believe that stable and steady situations, probably easy to capture by linearization, are paradisiacal, but already after a short period of everyday routine we usually become bored and seek change, that is, nonlinearities. If we reflect for a while, we notice that our life and our perceptions are mainly determined by nonlinear phenomena, for example, even...