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Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity)

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Synopses & Reviews

Publisher Comments:

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 mathematical theory.

In the twenty years since the first edition of this book appeared, the ideas and techniques of nonlinear dynamics and chaos have found application to such exciting new fields as systems biology, evolutionary game theory, and sociophysics. This second edition includes new exercises on these cutting-edge developments, on topics as varied as the curiosities of visual perception and the tumultuous love dynamics in Gone With the Wind.

Synopsis:

An accessible introduction to chaos and nonlinear systems, with numerous examples, illustrations, and applications to science and engineering.

Synopsis:

This textbook introduces chaos and nonlinear systems to students taking a first course in the subject. Richly illustrated, the second edition includes updated examples, illustrations and applications to science and engineering. 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.

About the Author

Steven Strogatz is a professor of Applied Mathematics at Cornell University. Hes known not only for his groundbreaking work in chaos and complexity theory, but also for making mathematics accessible and interesting to non-mathematicians. He received MITs highest teaching award, and is a recipient of the White Houses Presidential Young Investigator Award.

Table of Contents

Preface

1. Overview

1.0 Chaos, Fractals, and Dynamics

1.1 Capsule History of Dynamics

1.2 The Importance of Being Nonlinear

1.3 A Dynamical View of the World

PART I. ONE-DIMENSIONAL FLOWS

2. Flows on the Line

2.0 Introduction

2.1 A Geometric Way of Thinking

2.2 Fixed Points and Stability

2.3 Population Growth

2.4 Linear Stability Analysis

2.5 Existence and Uniqueness

2.6 Impossibility of Oscillations

2.7 Potentials

2.8 Solving Equations on the Computer

      Exercises

3. Bifurcations

3.0 Introduction

3.1 Saddle-Node Bifurcation

3.2 Transcritical Bifurcation

3.3 Laser Threshold

3.4 Pitchfork Bifurcation

3.5 Overdamped Bead on a Rotating Hoop

3.6 Imperfect Bifurcations and Catastrophes

3.7 Insect Outbreak

      Exercises

4. Flows on the Circle

4.0 Introduction

4.1 Examples and Definitions

4.2 Uniform Oscillator

4.3 Nonuniform Oscillator

4.4 Overdamped Pendulum

4.5 Fireflies

4.6 Superconducting Josephson Junctions

      Exercises

PART II. TWO-DIMENSIONAL FLOWS

5. Linear Systems

5.0 Introduction

5.1 Definitions and Examples

5.2 Classification of Linear Systems

5.3 Love Affairs

      Exercises

6. Phase Plane

6.0 Introduction

6.1 Phase Portraits

6.2 Existence, Uniqueness, and Topological Consequences

6.3 Fixed Points and Linearization

6.4 Rabbits versus Sheep

6.5 Conservative Systems

6.6 Reversible Systems

6.7 Pendulum

6.8 Index Theory

      Exercises

7. Limit Cycles

7.0 Introduction

7.1 Examples

7.2 Ruling Out Closed Orbits

7.3 Poincaré-Bendixson Theorem

7.4 Liénard Systems

7.5 Relaxation Oscillators

7.6 Weakly Nonlinear Oscillators

      Exercises

8. Bifurcations Revisited

8.0 Introduction

8.1 Saddle-Node, Transcritical, and Pitchfork Bifurcations

8.2 Hopf Bifurcations

8.3 Oscillating Chemical Reactions

8.4 Global Bifurcations of Cycles

8.5 Hysteresis in the Driven Pendulum and Josephson Junction

8.6 Coupled Oscillators and Quasiperiodicity

8.7 Poincaré Maps

      Exercises

PART III. CHAOS

9. Lorenz Equations

9.0 Introduction

9.1 A Chaotic Waterwheel

9.2 Simple Properties of the Lorenz Equations

9.3 Chaos on a Strange Attractor

9.4 Lorenz Map

9.5 Exploring Parameter Space

9.6 Using Chaos to Send Secret Messages

      Exercises

10. One-Dimensional Maps

10.0 Introduction

10.1 Fixed Points and Cobwebs

10.2 Logistic Map: Numerics

10.3 Logistic Map: Analysis

10.4 Periodic Windows

10.5 Liapunov Exponent

10.6 Universality and Experiments

10.7 Renormalization

        Exercises

11. Fractals

11.0 Introduction

11.1 Countable and Uncountable Sets

11.2 Cantor Set

11.3 Dimension of Self-Similar Fractals

11.4 Box Dimension

11.5 Pointwise and Correlation Dimensions

        Exercises

12. Strange Attractors

12.0 Introductions

12.1 The Simplest Examples

12.2 Hénon Map

12.3 Rössler System

12.4 Chemical Chaos and Attractor Reconstruction

12.5 Forced Double-Well Oscillator

        Exercises

Answers to Selected Exercises

References

Author Index

Subject Index

Product Details

ISBN:
9780813349107
Author:
Strogatz, Steven H.
Publisher:
Westview Press
Subject:
General Mathematics
Subject:
Mathematics-Calculus
Copyright:
Edition Description:
Second Edition, Second Edition
Series:
Studies in Nonlinearity
Publication Date:
20140731
Binding:
TRADE PAPER
Language:
English
Pages:
528
Dimensions:
9 x 6 in

Related Subjects

Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Popular Chaos and Fractals
Science and Mathematics » Physics » General

Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity) New Trade Paper
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Product details 528 pages Westview Press - English 9780813349107 Reviews:
"Synopsis" by ,
An accessible introduction to chaos and nonlinear systems, with numerous examples, illustrations, and applications to science and engineering.
"Synopsis" by ,
This textbook introduces chaos and nonlinear systems to students taking a first course in the subject. Richly illustrated, the second edition includes updated examples, illustrations and applications to science and engineering. 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.
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