Introduction to Nonlinear Science

Introduction to Nonlinear Science

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The aim of this book is to develop a unified approach to nonlinear science, which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Nonlinear science emerged in its present form following a series of closely related and decisive analytic, numerical and experimental developments that took place over the past three decades. It appeals to an extremely large variety of subject areas, but, at the same time, introduces into science a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, topological and metric considerations and deterministic and statistical views. Special effort has been made throughout the book to illustrate both the development of the subject and the mathematical techniques, by reference to simple models. Each chapter concludes with a set of problems. This book will be of great value to graduate students in physics, applied mathematics, chemistry, engineering and biology taking courses in nonlinear science and its applications.
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"...this book can be recommended to graduate students and researchers for independent study as well as being a basis for an advanced undergraduate course." Moshe Gitterman, Journal of Statistical Physics "What has been achieved is success in placing the key ideas involved within a wide framework involving many different parts of science. In this the author is to be congratulated..." Eric Renshaw, Bulletin of Mathematical Biology "Introduction to Nonlinear Science will be a very valuable addition to the libraries of serious nonlinear dynamics students, and the author is to be commended for making an important contribution to the field." D.T. Mook, Applied Mechanics Review
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Table of contents

Preface; 1. Nonlinear behavior in the physical sciences and biology: some typical examples; 2. Quantitative formulation; 3. Dynamical systems with a finite number of degrees of freedom; 4. Linear stability analysis of fixed points; 5. Nonlinear behavior around fixed points: bifurcation analysis; 6. Spatially distributed systems, broken symmetries, pattern formation; 7. Chaotic dynamics; Appendices; References; Index.
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