Nonlinear Dynamics and Chaos

ISBN-13: 9780471876458 / Angielski / Twarda / 2002 / 460 str.

Michael Thompson; J. M. T. Thompson; H. B. Stewart

Opis

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

Recenzje

??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)

Spis treści

Preface.

Preface to the First Edition.

Acknowledgements from the First Edition.

Introduction

PART I: 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

PART II ITERATED MAPS AS DYNAMICAL SYSTEMS

Stability and bifurcation of maps

Chaotic behaviour of one–and two–dimensional maps

PART III FLOWS, OUTSTRUCTURES AND CHAOS

The Geometry of Recurrence

The Lorenz system

Rosslers band

Geometry of bifurcations

PART IV APPLICATIONS IN THE PHYSICAL SCIENCES

Subharmonic resonances of an offshore structure

Chaotic motions of an impacting system

Escape from a potential well

Appendix.

Illustrated Glossary.

Bibliography.

Online Resource.

Index.

Blurb

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.