3rd Edition
Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry, and Engineering
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
Chapter 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
Chapter 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 for Chapter 2
Chapter 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 for Chapter 3
Chapter 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 for Chapter 4
Part II Two-Dimensional Flows
Chapter 5 Linear Systems
5.0 Introduction
5.1 Definitions and Examples
5.2 Classification of Linear Systems
5.3 Love Affairs
Exercises for Chapter 5
Chapter 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 for Chapter 6
Chapter 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 Oscillations
7.6 Weakly Nonlinear Oscillators
Exercises for Chapter 7
Chapter 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 for Chapter 8
Part III Chaos
Chapter 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 for Chapter 9
Chapter 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 for Chapter 10
Chapter 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 for Chapter 11
Chapter 12 Strange Attractors
12.0 Introduction
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 for Chapter 12
Part IV Collective Behavior
Chapter 13 Kuramoto Model
13.0 Introduction
13.1 Governing Equations
13.2 Visualization and the Order Parameter
13.3 Mean-Field Coupling and Rotating Frame
13.4 Steady State
13.5 Self-Consistency
13.6 Remaining Questions
Exercises for Chapter 13
Answers to Selected Exercises
References
Author Index
Subject Index
Biography
Steven Strogatz is the Schurman Professor of Applied Mathematics at Cornell University. His honors include MIT's highest teaching prize, a lifetime achievement award for the communication of mathematics to the general public, and membership in the American Academy of Arts and Sciences. His research on a wide variety of nonlinear systems from synchronized fireflies to small-world networks has been featured in the pages of Scientific American, Nature, Discover, Business Week, and The New York Times.
