Nonlinear Dynamics and Chaos - Strogatz.pdf-资料库

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第1页.png

第1页 / 共505页

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第2页.png

第2页 / 共505页

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第3页.png

第3页 / 共505页

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第4页.png

第4页 / 共505页

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第5页.png

第5页 / 共505页

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第6页.png

第6页 / 共505页

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第7页.png

第7页 / 共505页

weixin_42381005-10508362-Nonlinear Dynamics and Chaos - Strogatz.pdf-第8页.png

第8页 / 共505页

STUDIES IN NONLINEARITY N�ONLJNEAR DYNAMICS ANDCHAOS' . . With Applications to Physics, Biology, Chemistry, and Engineering STEVEN� H.: STROGATZ

-- NONLINEAR DYNAMICS AND CHAOS With Applications Physics, Biology, and Engineering to Chemistry, STEVEN H. STROGATZ ADVANCED BOOK PROGRAM PERSEUS BOOKS setts Reading, Massachu

used by manufacturers Many of the designations guish their products tions appear in this book and Perseus Books was aware of a trademark claim, the designations to distin Where those designa have been printed in initial capital letters. are claimed as trademarks. and sellers Library of Congress Cataloging-in- Strogatz, Steven H. (Steven Henry) Publication Data Nonlinear biology, chemistry, dynamics and chaos: with applications I Steven H. Strogatz. and engineering to physics, p. cm. Includes bibliographical ISBN 0-201-54344-3 I. Chaotic behavior in systems. 2. Dynamics. references and index. 3. Nonlinear I. Title. theories. QI72.5.C45S767 501'.1'85-dc20 1994 93-6166 CIP Copyright © 1994 by Perseus Books Publishing, L.L.c. Perseus Books is a member of the Perseus Books Group. All rights reserved. stored in a retrieval electronic, the prior written permission of America. Published meehanical, No part of this publication system, or transmitted, photocopying, recording, in any form or by any means, without or otherwise, may be reproduced, of the publisher. Printed in the United States simultaneously in Canada. Times by Compset, Inc. Cover design by Lynne Reed Text design by Joyce C. Weston Set in 10-point Cover art is a computer-generated Strogatz (1985) with permission. Scroll sources of waves in diverse excitable neural tissue, 1984, Winfree 1987b). chemical reactions and excitable picture of a scroll ring, from rings are self-sustaining media, including heart muscle, (Winfree and Strogatz 10 11 12 13 14 15-MA-03 02 01 00 99 Perseus Books are U.S. by corporations, formation, Collins Publishers, 212-207-7528. available for special discounts for bulk institutions, and other organizations. purchases For more in in the please contact the Special Markets Department at Harper 10 East 53rd Street, New York, NY 10022, or call 1-

C ONTENTS Preface ix 1. Overview 1 1 .0 Chaos, Fractals, and Dynamics of Dynamics 2 1 . 1 Capsule 1 .2 The Importance of 4 1 .3 A Dynamical View of the World 9 History Being Nonlinear Part I. One-Dimensional Flows 1 6 Way of Thinking and Stability 1 8 Analysis 24 26 2. Flows on the Line 15 1 5 Growth 2 1 2.0 Introduction 2.1 A Geometric 2.2 Fixed Points 2.3 Population 2.4 Linear Stability 2.5 Existence 2.6 Impossibility 2.7 Potentials 30 2.8 Solving Exercises 36 3. Bifurcations 44 Equations and Uniqueness of Oscillations 28 on the Computer 32 44 Bifurcation 45 Bifurcation 50 3.0 Introduction 3 . 1 Saddle-Node 3.2 Transcritical 3.3 Laser Threshold 5 3 3.4 Pitchfork 3.5 Overdamped Bifurcation 5 5 B ead on a Rotating Hoop 61 CONTENTS v

3.6 Imperfect Bifurcations 3.7 Insect Outbreak 73 and Catastrophes 69 Exercises 79 4. Flows on the Circle 93 4.0 Introduction 93 4.1 Examples and Definitions 93 4.2 Uniform Oscillator 4.3 Nonuniform Oscillator 96 4.4 Overdamped Pendulum 101 4.5 Fireflies 103 4.6 Superconducting 95 Josephson Junctions 106 Exercises 113 Part II. Two-Dimensional Flows Linear Systems 123 5.0 Introduction 123 5.1 Definitions 5.2 Classification 5.3 Love Affairs 138 Exercises 140 and Examples 123 of Linear Systems 129 5. 6. and Topological Consequences 148 145 145 Uniqueness, Phase Plane 145 6.0 Introduction 6.1 Phase Portraits 6.2 Existence, 6.3 Fixed Points and Linearization 150 6.4 Rabbits versus Sheep 155 6.5 Conservative Systems 159 6.6 Reversible 6.7 Pendulum 168 6.8 Index Theory 174 Systems 163 Exercises 181 7. Limit Cycles 196 7.0 Introduction 196 7.1 Examples 197 7.2 Ruling Out Closed Orbits 199 7.3 Poincare-Bendixson 7.4 Lienard Systems 210 7.5 Relaxation 7.6 Weakly Nonlinear Oscillators 215 Oscillators 211 Theorem 203 Exercises 227 vi CONTENTS

8. Bifurcations Revisited 241 t ion 241 8.0 Introduc 8.1 Saddle-Node, Transcrit ical, and P itchfork B ifurcations 241 8.2 Hopf B ifurcations 248 8.3 Oscillating Chemical Reactions 254 8.4 Global B ifurcations of C ycles 260 8.5 H ysteresis in the Driven Pendulum 8.6 Coupled 8.7 Poincare Maps 278 Oscillators and Quasiperiodic it y 273 and Josephson Junction 265 Exercises 284 Part III. Chaos 9. Lorenz Equations 301 9.0 Introduction 301 9.1 A Chaotic Waterwheel 9.2 S imple Properties of the 9.3 Chaos on a Strange 9.4 Lorenz Map 326 9.5 Explori 9.6 Using Chaos to Send ng Parameter Space 330 Secret 302 Lorenz Equations 31 I Attractor 317 Messages 335 Exercises 341 10. Maps 348 ction 348 One-Dimensional 10.0 Introdu 10.1 F ixed Points and Cobwebs 349 10.2 Logistic Map: Numerics 353 10.3 Log istic Map : Analys is 357 10.4 Period ic W indows 361 10.5 L iapunov Exponent 366 10.6 Universality and Experiments 10.7 Renormalization 379 369 Exercises 388 11. Fractals 398 11.0 Introduct ion 398 11.1 Countable and Uncountable II .2 Cantor 11.3 D imension o f Self-Similar Fractals 404 11.4 B ox D imension 409 11.5 Pointwise and Correlation D imensions 411 Set 40 I Sets 399 Exercises 416 C O N T E N T S vii

12. Strange Attractors 423 t ion 423 12.0 Introduc 12.1 The S implest Examp l es 423 12.2 Henon Map 429 12.3 R ossler S ystem 434 12.4 Chem ical Chaos and Attractor 12.5 Forced Double-Well Oscillator 441 R econstructi on 437 Exercis es 448 Answers to Selected Exercises 455 References 465 Author Index 475 Subject Index 478 viii C O NTENTS

PREFACE a first course in the subject. It is based on a one-semester course is aimed at newcomers to nonlinear dynamics This textbook students taking I've taught for the past several mathematics some of the wonders years at MIT and CornelL of the nonlinear world. as possible, as clearly and to show how it can be used My goal is to explain the to understand and chaos, especially The mathematical treatment is friendly and informal, but still careful. Analyti systemat cal methods, developed bifurcat and culminating renormalizat ions, followed ion, fractals, concrete examples, and geometric intuition are stressed. The theory is ically, starting with first-order differential equations by phase plane analysis, limit cycles with the Lorenz equation s, chaos, iterated and their and their bifurcations, maps, period doubling, and strange attractors. A unique feature of the book is its emphasis on applicat ions. These include me chanical vibrations, lasers, outbreaks, chemical even a technique entific the mathematical background theory. oscilla biological superconducting circuits, insect tors, genetic systems, chaotic rhythms, control waterwheels, and each case, the sci for using chaos to send secret messages. In integrated with ry level and closely is explained at an elementa Prerequisites prerequi site is single-va The essential (partial derivatives, Jacobian riable ing, Taylor series, and separable differential able calculus algebra and is developed where needed. scientific cases, prerequisites a first course should and eigenvectors) (eigenvalues be adequate preparat ion. calculus, equations. In divergence including a few places, theorem) matrix, multivari and linear curve-sketch are used. Fourier analysis is not assumed, Introductory physics is used throughout. Other would depend on the applications considered, but in all PREFACE ix

资料库

Nonlinear Dynamics and Chaos - Strogatz.pdf

相关推荐

课程资源

热门标签

最新资料