Synopses & Reviews
Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists J. M. T. Thompson, FRS, University College, London H. B. Stewart, Brookhaven National Laboratory This book is the first comprehensive, systematic account of nonlinear dynamics and chaos, one of the fastest-growing disciplines of applicable mathematics. It is highly illustrated and written in a clear, comprehensible style, progressing gently from the most elementary to the most advanced ideas while requiring little previous knowledge of mathematics. Examples of applications to a wide variety of scientific fields introduce concepts of instabilities, bifurcations and catastrophes, and particular attention is given to the vital new ideas of chaotic behaviour and unpredictability in deterministic systems. This is a book for systems analysts, for mathematicians, and for all those in any field of science or technology who use computers to model systems which change over time. Contents Preface 1 Introduction Part I Basic Concepts of Nonlinear Dynamics 2 An overview of nonlinear phenomena; 3 Point attractors in autonomous systems; 4 Limit cycles in autonomous systems; 5 Periodic attractors in driven oscillators; 6 Chaotic attractors in forced oscillators; 7 Stability and bifurcations of equilibria and cycles Part II Iterated Maps as Dynamical Systems 8 Stability and bifurcation of maps; 9 Chaotic behaviour of one- and two-dimensional maps Part III Flows, Outstructures, and Chaos 10 The geometry of recurrence; 11 The Lorenz system; 12 Rösslers band; 13 Geometry of bifurcation Part IV Applications in the Physical Sciences 14 Subharmonic resonances of an offshore structure; 15 Chaotic motions of an impacting system; 16 The particle accelerator and Hamiltonian dynamics; 17 Experimental observations of order and chaos References and Bibliography Index
Review
??much more extensive than before..? (The Mathematical Review, March 2004)
"The fully updated second edition provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos." (International Journal of Environmental Analytical Chemistry, Vol.84, No.14 – 15, 10 – 20 December 2004)
Synopsis
Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos.
* Expands on the bestselling, highly regarded first edition
* A new chapter which will cover the new research in the area since first edition
* Glossary of terms and a bibliography have been added
* All figures and illustrations will be 'modernised'
* Comprehensive and systematic account of nonlinear dynamics and chaos, still a fast-growing area of applied mathematics
* Highly illustrated
* Excellent introductory text, can be used for an advanced undergraduate/graduate course text
Synopsis
Covering one of the fastest growing areas of applied mathematics,
Nonlinear Dynamics and Chaos: Second Edition, is a fully updated edition of this highly respected text. Covering a breadth of topics, ranging from the basic concepts to applications in the physical sciences, the book is highly illustrated and written in a clear and comprehensible style. <>
Provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos. Introduces the concepts of instabilities, bifurcations, and catastrophes. Each idea is carefully explained and supported by examples. Features many applications to a wide variety of scientific fields. Includes an illustrated glossary of geometrical dynamics. Features a supplementary bibliography of further reading. Assumes minimal background knowledge. Nonlinear Dynamics and Chaos: Second Edition provides an excellent introduction to the subject for students of mathematics, engineering, physics and applied science. It will also appeal to the many researchers who work with computer models of systems that change over time. Table of Contents
Introduction.
BASIC CONCEPTS OF NONLINEAR DYNAMICS.
An Overview of Nonlinear Phenomena.
Point Attractors in Autonomous Systems.
Limit Cycles in Autonomous Systems.
Periodic Attractors in Driven Oscillators.
Chaotic Attractors in Forced Oscillators.
Stability and Bifurcations of Equilibria and Cycles.
ITERATED MAPS AS DYNAMICAL SYSTEMS.
Stability and Bifurcation of Maps.
Chaotic Behaviour of One and Two-Dimensional Maps.
FLOWS, OUTSTRUCTURES AND CHAOS.
The Geometry of Recurrence.
The Lorenz System.
Rossler's Band.
Geometry of Bifurcations.
APPLICATIONS IN THE PHYSICAL SCIENCES.
Subharmonic Resonances of an Off-Shore Structure.
Chaotic Motions of An Impacting System.
The Particle Accelerator and Beam-Beam Interaction.
Experimental Observations of Order and Chaos (H. L. Swinney).
Bibliography.
Index.