Nonlinear Dynamics and Chaos: Geometrical Methods for Engineers and Scientists

by H.B. Stewart, J.M.T. Thompson, H. B. Stewart

Book Overview

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 ROssler's 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

• Format: Hardcover
• Language: English
• ISBN: 0471909602
• ISBN13: 9780471909606
• Release Date: August 1986
• Publisher: Wiley
• Length: 392 Pages
• Weight: 1.50 lbs.
• Dimensions: 1.1" x 6.2" x 9.3"

Customer Reviews

Good Introduction To Chaos

The book is complex enough to provide good information on NLD, chaos, and the associated differential equations, but not so complex you can't get a firm working grasp of the subject. Lots of nice illustrations, clearly and concisely explained. Bifurcations, attractors and all that jazz is in there too if you want to make your own Poincare maps (also explained). I used the information from the book to generate visualizations of an externally excited system moving in and out of different modes of vibration. Such a techinique is not directly explaned in the text, but a good read of the first few chapters will provide the tools to do so. Recommended.