Nonlinear Dynamics and Chaos: With Applications in Physics, Biology, Chemistry, and Engineering

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Overview

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.A unique feature of the book is its emphasis on applications. These include mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory.Richly illustrated, and with many exercises and worked examples, this book is ideal for an introductory course at the junior/senior or first-year graduate level. It is also ideal for the scientist who has not had formal instruction in nonlinear dynamics, but who now desires to begin informal study. The prerequisites are multivariable calculus and introductory physics.

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Editorial Reviews

Booknews
Intended as a first course in nonlinear dynamics and chaos, the presentation stresses analytical methods, concrete examples, and geometric intuition. Applications are emphasized, including mechanical vibrations, lasers, biological rhythms, superconducting circuits, insect outbreaks, chemical oscillators, genetic control systems, chaotic waterwheels, and even secret messages. Many worked examples and exercises with selected answers are included. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780201543445
  • Publisher: Westview Press
  • Publication date: 4/1/1994
  • Series: Studies in Nonlinearity
  • Pages: 498
  • Product dimensions: 6.40 (w) x 9.52 (h) x 1.27 (d)

Table of Contents

Preface
1 Overview 1
Pt. I One-Dimensional Flows
2 Flows on the Line 15
3 Bifurcations 44
4 Flows on the Circle 93
Pt. II Two-Dimensional Flows
5 Linear Systems 123
6 Phase Plane 145
7 Limit Cycles 196
8 Bifurcations Revisited 241
Pt. III Chaos
9 Lorenz Equations 301
10 One-Dimensional Maps 348
11 Fractals 398
12 Strange Attractors 423
Answers to Selected Exercises 455
References 465
Author Index 475
Subject Index 478
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