| Preface to the Third Edition | p. ix |
| Preface | p. xi |
| First-Order Equations | p. 1 |
| The Simplest Example | p. 1 |
| The Logistic Population Model | p. 4 |
| Constant Harvesting and Bifurcations | p. 7 |
| Periodic Harvesting and Periodic Solutions | p. 10 |
| Computing the Poincaré Map | p. 11 |
| Exploration: A Two-Parameter Family | p. 15 |
| Planar Linear Systems | p. 21 |
| Second-Order Differential Equations | p. 23 |
| Planar Systems | p. 24 |
| Preliminaries from Algebra | p. 26 |
| Planar Linear Systems | p. 29 |
| Eigenvalues and Eigenvectors | p. 30 |
| Solving Linear Systems | p. 33 |
| The Linearity Principle | p. 36 |
| Phase Portraits for Planar Systems | p. 39 |
| Real Distinct Eigenvalues | p. 39 |
| Complex Eigenvalues | p. 44 |
| Repeated Eigenvalues | p. 47 |
| Changing Coordinates | p. 49 |
| Classification of Planar Systems | p. 61 |
| The Trace-Determinant Plane | p. 61 |
| Dynamical Classification | p. 64 |
| Exploration: A 3D Parameter Space | p. 71 |
| Higher-Dimensional Linear Algebra | p. 73 |
| Preliminaries from Linear Algebra | p. 73 |
| Eigenvalues and Eigenvectors | p. 82 |
| Complex Eigenvalues | p. 85 |
| Bases and Subspaces | p. 88 |
| Repeated Eigenvalues | p. 93 |
| Genericity | p. 100 |
| Higher-Dimensional Linear Systems | p. 107 |
| Distinct Eigenvalues | p. 107 |
| Harmonic Oscillators | p. 114 |
| Repeated Eigenvalues | p. 120 |
| The Exponential of a Matrix | p. 123 |
| Nonautonomous Linear Systems | p. 130 |
| Nonlinear Systems | p. 139 |
| Dynamical Systems | p. 140 |
| The Existence and Uniqueness Theorem | p. 142 |
| Continuous Dependence of Solutions | p. 147 |
| The Variational Equation | p. 149 |
| Exploration: Numerical Methods | p. 153 |
| Exploration: Numerical Methods and Chaos | p. 156 |
| Equilibria in Nonlinear Systems | p. 159 |
| Some Illustrative Examples | p. 159 |
| Nonlinear Sinks and Sources | p. 165 |
| Saddles | p. 168 |
| Stability | p. 174 |
| Bifurcations | p. 175 |
| Exploration: Complex Vector Fields | p. 182 |
| Global Nonlinear Techniques | p. 187 |
| Nullclines | p. 187 |
| Stability of Equilibria | p. 192 |
| Gradient Systems | p. 202 |
| Hamiltonian Systems | p. 206 |
| Exploration: The Pendulum with Constant Forcing | p. 209 |
| Closed Orbits and Limit Sets | p. 213 |
| Limit Sets | p. 213 |
| Local Sections and Flow Boxes | p. 216 |
| The Poincaré Map | p. 218 |
| Monotone Sequences in Planar Dynamical Systems | p. 220 |
| The Poincaré-Bendixson Theorem | p. 222 |
| Applications of Poincaré-Bendixson | p. 225 |
| Exploration: Chemical Reactions that Oscillate | p. 228 |
| Applications in Biology | p. 233 |
| Infectious Diseases | p. 233 |
| Predator-Prey Systems | p. 237 |
| Competitive Species | p. 244 |
| Exploration: Competition and Harvesting | p. 250 |
| Exploration: Adding Zombies to the SIR Model | p. 251 |
| Applications in Circuit Theory | p. 257 |
| An RLC Circuit | p. 257 |
| The Liénard Equation | p. 261 |
| The van der Pol Equation | p. 263 |
| A Hopf Bifurcation | p. 270 |
| Exploration: Neurodynamics | p. 272 |
| Applications in Mechanics | p. 277 |
| Newton's Second Law | p. 277 |
| Conservative Systems | p. 280 |
| Central Force Fields | p. 282 |
| The Newtonian Central Force System | p. 285 |
| Kepler's First Law | p. 290 |
| The Two-Body Problem | p. 293 |
| Blowing Up the Singularity | p. 294 |
| Exploration: Other Central Force Problems | p. 298 |
| Exploration: Classical Limits of Quantum Mechanical Systems | p. 299 |
| Exploration: Motion of a Glider | p. 301 |
| The Lorenz System | p. 305 |
| Introduction | p. 306 |
| Elementary Properties of the Lorenz System | p. 308 |
| The Lorenz Attractor | p. 312 |
| A Model for the Lorenz Attractor | p. 316 |
| The Chaotic Attractor | p. 321 |
| Exploration: The Rössler Attractor | p. 326 |
| Discrete Dynamical Systems | p. 329 |
| Introduction | p. 329 |
| Bifurcations | p. 334 |
| The Discrete Logistic Model | p. 337 |
| Chaos | p. 340 |
| Symbolic Dynamics | p. 344 |
| The Shift Map | p. 349 |
| The Cantor Middle-Thirds Set | p. 351 |
| Exploration: Cubic Chaos | p. 354 |
| Exploration: The Orbit Diagram | p. 355 |
| Homoclinic Phenomena | p. 361 |
| The Shilnikov System | p. 361 |
| The Horseshoe Map | p. 368 |
| The Double Scroll Attractor | p. 375 |
| Homoclinic Bifurcations | p. 377 |
| Exploration: The Chua Circuit | p. 381 |
| Existence and Uniqueness Revisited | p. 385 |
| The Existence and Uniqueness Theorem | p. 385 |
| Proof of Existence and Uniqueness | p. 387 |
| Continuous Dependence on Initial Conditions | p. 394 |
| Extending Solutions | p. 397 |
| Nonautonomous Systems | p. 401 |
| Differentiability of the Flow | p. 404 |
| Bibliography | p. 411 |
| Index | p. 415 |
| Table of Contents provided by Ingram. All Rights Reserved. |
