Normal Modes and Localization in Nonlinear Systems

This book provides its reader with a good understanding of the stabilization of switched nonlinear systems (SNS), systems that are of practical use in diverse situations: design of fault-tolerant syst

This book contains a collection of original papers on nonlinear normal modes and localization in dynamical systems from leading experts in the field. The reader will find new analytical and computatio

This book covers quantum mechanics in macroscopic systems, focusing on quantum fluctuations and localization by quantum interference. Based on elementary quantum and statistical physics, the book poin

This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many new developments.Whil

Localization and tracking are key functionalities in ubiquitous computing systems and techniques. In recent years a very high variety of approaches, sensors and techniques for indoor and GPS-denied en

The book reports on the latest advances and applications of nonlinearcontrol systems. ?It consists of 30contributed chapters by subject experts who are specialized in the varioustopics addressed in th

In this book, editor Lyubomir T. Gruyitch presents readers with an examination of the theory and practice of tracking, trackability, and tracking control synthesis for nonlinear processes and their va

Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

Analytical Periodic Flows and Chaos in Nonlinear Systems systematically presents a new approach to analytically determine the periodic flows and chaos in nonlinear dynamical systems.The new analytical

Discontinuity in Nonlinear Physical Systems explores recent developments in experimental research in this broad field, organized in four distinct sections. Part I introduces the reader to the fraction

With many areas of science reaching across their boundaries and becoming more and more interdisciplinary, students and researchers in these fields are confronted with techniques and tools not covered

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in th

Nonlinear Waves in Integrable and Nonintegrable Systems presents cutting-edge developments in the theory and experiments of nonlinear waves. Its comprehensive coverage of analytical and numerical meth

Intended for first-year graduate students in engineering and mathematics in courses in nonlinear systems or control, this text may also be used for self-study or reference by engineers and applied mat

This book provides an introduction to the analysis of chaos and chaos theory as it relates to agricultural science. With clear explanations of chaos theory and principles, the first part of the book o

Designed for one-semester introductory senior-or graduate-level course, the authors provide the student with an introduction of analysis techniques used in the design of nonlinear and optimal feedback

The theories of bifurcation, chaos and fractals as well as equilibrium, stability and nonlinear oscillations, are part of the theory of the evolution of solutions of nonlinear equations. A wide range of mathematical tools and ideas are drawn together in the study of these solutions, and the results applied to diverse and countless problems in the natural and social sciences, even philosophy. The text evolves from courses given by the author in the UK and the United States. It introduces the mathematical properties of nonlinear systems, mostly difference and differential equations, as an integrated theory, rather than presenting isolated fashionable topics. Topics are discussed in as concrete a way as possible and worked examples and problems are used to explain, motivate and illustrate the general principles. The essence of these principles, rather than proof or rigour, is emphasized. More advanced parts of the text are denoted by asterisks, and the mathematical prerequisites are limit

Nonlinear Systems and Their Remarkable Mathematical Structures aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete).

This brief provides an overview on the most relevant nonlinear phenomena in internal combustion engines with a particular emphasis on the use of nonlinear circuits in their modelling and control. The

The book investigates stability theory in terms of two different measure, exhibiting the advantage of employing families of Lyapunov functions and treats the theory of a variety of inequalities, clear

Written when the young science of chaos was gaining a foothold in the scientific community, this book introduces the field's concepts, applications, theory, and technique. Suitable for advanced underg

This book provides a comprehensive treatment of the Gross–Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose–Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrödinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrödinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross–Pitaevskii equation. It also serves as a reference for theoretical physicists inter

Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The third volume deals with experimental aspects of the study of noise in nonlinear dynamical systems. It covers noise-driven phenomena in superfluid helium, liquid crystals, lasers and optical bistability as well as the solution of stochastic equations by digital simula

This is the first book on a hot topic in the field of control of nonlinear systems. It ranges from mathematical system theory to practical industrial control applications and addresses two fundamental

This monograph is the first in the new area of targeted nonlinear energy transfer in mechanical and structural systems. This concept was initially discovered by the two leading authors in 1999, and w

While many books have discussed methodological advances in nonlinear dynamical systems theory (NDS), this volume is unique in its focus on NDS's role in the development of psychological theory. After an introductory chapter covering the fundamentals of chaos, complexity and other nonlinear dynamics, subsequent chapters provide in-depth coverage of each of the specific topic areas in psychology. A concluding chapter takes stock of the field as a whole, evaluating important challenges for the immediate future. The chapters are written by experts in the use of NDS in each of their respective areas, including biological, cognitive, developmental, social, organizational and clinical psychology. Each chapter provides an in-depth examination of theoretical foundations and specific applications and a review of relevant methods. This edited collection represents the state of the art in NDS science across the disciplines of psychology.

In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the pre

The chapters of this book have been presented at the 1st Workshop of the Nonlinear Control Network*, which was held in Ghent, March 15,16, 1999. These contributions give an overview of some of the cur

There has been much excitement over the emergence of new mathematical techniques for the analysis and control of nonlinear systems. In addition, great technological advances have bolstered the impact

In electronic circuit and system design, the word noise is used to refer to any undesired excitation on the system. In other contexts, noise is also used to refer to signals or excitations which exhib