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| Preface | |
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| First-Order Equations | |
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| The Simplest Example | |
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| The Logistic Population Model | |
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| Constant Harvesting and Bifurcations | |
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| Periodic Harvesting and Periodic Solutions | |
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| Computing the Poincare Map | |
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| Exploration: A Two-Parameter Family | |
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| Planar Linear Systems | |
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| Second-Order Differential Equations | |
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| Planar Systems | |
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| Preliminaries from Algebra | |
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| Planar Linear Systems | |
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| Eigenvalues and Eigenvectors | |
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| Solving Linear Systems | |
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| The Linearity Principle | |
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| Phase Portraits for Planar Systems | |
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| Real Distinct Eigenvalues | |
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| Complex Eigenvalues | |
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| Repeated Eigenvalues | |
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| Changing Coordinates | |
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| Classification of Planar Systems | |
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| The Trace-Determinant Plane | |
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| Dynamical Classification | |
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| Exploration: A 3D Parameter Space | |
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| Higher Dimensional Linear Algebra | |
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| Preliminaries from Linear Algebra | |
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| Eigenvalues and Eigenvectors | |
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| Complex Eigenvalues | |
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| Bases and Subspaces | |
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| Repeated Eigenvalues | |
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| Genericity | |
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| Higher Dimensional Linear Systems | |
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| Distinct Eigenvalues | |
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| Harmonic Oscillators | |
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| Repeated Eigenvalues | |
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| The Exponential of a Matrix | |
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| Nonautonomous Linear Systems | |
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| Nonlinear Systems | |
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| Dynamical Systems | |
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| The Existence and Uniqueness Theorem | |
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| Continuous Dependence of Solutions | |
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| The Variational Equation | |
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| Exploration: Numerical Methods | |
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| Equilibria in Nonlinear Systems | |
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| Some Illustrative Examples | |
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| Nonlinear Sinks and Sources | |
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| Saddles | |
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| Stability | |
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| Bifurcations | |
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| Exploration: Complex Vector Fields | |
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| Global Nonlinear Techniques | |
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| Nullclines | |
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| Stability of Equilibria | |
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| Gradient Systems | |
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| Hamiltonian Systems | |
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| Exploration: The Pendulum with Constant Forcing | |
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| Closed Orbits and Limit Sets | |
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| Limit Sets | |
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| Local Sections and Flow Boxes | |
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| The Poincare Map | |
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| Monotone Sequences in Planar Dynamical Systems | |
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| The Poincare-Bendixson Theorem | |
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| Applications of Poincare-Bendixson | |
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| Exploration: Chemical Reactions That Oscillate | |
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| Applications in Biology | |
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| Infectious Diseases | |
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| Predator/Prey Systems | |
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| Competitive Species | |
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| Exploration: Competition and Harvesting | |
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| Applications in Circuit Theory | |
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| An RLC Circuit | |
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| The Lienard Equation | |
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| The van der Pol Equation | |
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| A Hopf Bifurcation | |
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| Exploration: Neurodynamics | |
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| Applications in Mechanics | |
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| Newton's Second Law | |
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| Conservative Systems | |
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| Central Force Fields | |
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| The Newtonian Central Force System | |
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| Kepler's First Law | |
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| The Two-Body Problem | |
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| Blowing Up the Singularity | |
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| Exploration: Other Central Force Problems | |
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| Exploration: Classical Limits of Quantum Mechanical Systems | |
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| The Lorenz System | |
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| Introduction to the Lorenz System | |
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| Elementary Properties of the Lorenz System | |
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| The Lorenz Attractor | |
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| A Model for the Lorenz Attractor | |
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| The Chaotic Attractor | |
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| Exploration: The Rossler Attractor | |
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| Discrete Dynamical Systems | |
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| Introduction to Discrete Dynamical Systems | |
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| Bifurcations | |
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| The Discrete Logistic Model | |
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| Chaos | |
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| Symbolic Dynamics | |
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| The Shift Map | |
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| The Cantor Middle-Thirds Set | |
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| Exploration: Cubic Chaos | |
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| Exploration: The Orbit Diagram | |
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| Homoclinic Phenomena | |
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| The Shil'nikov System | |
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| The Horseshoe Map | |
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| The Double Scroll Attractor | |
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| Homoclinic Bifurcations | |
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| Exploration: The Chua Circuit | |
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| Existence and Uniqueness Revisited | |
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| The Existence and Uniqueness Theorem | |
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| Proof of Existence and Uniqueness | |
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| Continuous Dependence on Initial Conditions | |
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| Extending Solutions | |
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| Nonautonomous Systems | |
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| Differentiability of the Flow | |
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| Bibliography | |
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| Index | |