Nonlinear Dynamics and Chaos

Cover
Half Title
Title Page
Copyright Page
Contents
Preface to the Third Edition
Preface to the Second Edition
Preface to the First Edition
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
	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
	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
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
	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
	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
	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
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
	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
	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
	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
Part IV: Collective Behavior
	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
Answers to Selected Exercises
References
Author Index
Subject Index