Preface |
First-Order Equations / Chapter 1: |
The Simplest Example / 1.1: |
The Logistic Population Model / 1.2: |
Constant Harvesting and Bifurcations / 1.3: |
Periodic Harvesting and Periodic Solutions / 1.4: |
Computing the Poincare Map / 1.5: |
Exploration: A Two-Parameter Family / 1.6: |
Planar Linear Systems / Chapter 2: |
Second-Order Differential Equations / 2.1: |
Planar Systems / 2.2: |
Preliminaries from Algebra / 2.3: |
Eigenvalues and Eigenvectors / 2.4: |
Solving Linear Systems / 2.6: |
The Linearity Principle / 2.7: |
Phase Portraits for Planar Systems / Chapter 3: |
Real Distinct Eigenvalues / 3.1: |
Complex Eigenvalues / 3.2: |
Repeated Eigenvalues / 3.3: |
Changing Coordinates / 3.4: |
Classification of Planar Systems / Chapter 4: |
The Trace-Determinant Plane / 4.1: |
Dynamical Classification / 4.2: |
Exploration: A 3D Parameter Space / 4.3: |
Higher Dimensional Linear Algebra / Chapter 5: |
Preliminaries from Linear Algebra / 5.1: |
Bases and Subspaces / 5.2: |
Genericity / 5.5: |
Higher Dimensional Linear Systems / Chapter 6: |
Distinct Eigenvalues / 6.1: |
Harmonic Oscillators / 6.2: |
The Exponential of a Matrix / 6.3: |
Nonautonomous Linear Systems / 6.5: |
Nonlinear Systems / Chapter 7: |
Dynamical Systems / 7.1: |
The Existence and Uniqueness Theorem / 7.2: |
Continuous Dependence of Solutions / 7.3: |
The Variational Equation / 7.4: |
Exploration: Numerical Methods / 7.5: |
Equilibria in Nonlinear Systems / Chapter 8: |
Some Illustrative Examples / 8.1: |
Nonlinear Sinks and Sources / 8.2: |
Saddles / 8.3: |
Stability / 8.4: |
Bifurcations / 8.5: |
Exploration: Complex Vector Fields / 8.6: |
Global Nonlinear Techniques / Chapter 9: |
Nullclines / 9.1: |
Stability of Equilibria / 9.2: |
Gradient Systems / 9.3: |
Hamiltonian Systems / 9.4: |
Exploration: The Pendulum with Constant Forcing / 9.5: |
Closed Orbits and Limit Sets / Chapter 10: |
Limit Sets / 10.1: |
Local Sections and Flow Boxes / 10.2: |
The Poincare Map / 10.3: |
Monotone Sequences in Planar Dynamical Systems / 10.4: |
The Poincare-Bendixson Theorem / 10.5: |
Applications of Poincare-Bendixson / 10.6: |
Exploration: Chemical Reactions That Oscillate / 10.7: |
Applications in Biology / Chapter 11: |
Infectious Diseases / 11.1: |
Predator/Prey Systems / 11.2: |
Competitive Species / 11.3: |
Exploration: Competition and Harvesting / 11.4: |
Applications in Circuit Theory / Chapter 12: |
An RLC Circuit / 12.1: |
The Lienard Equation / 12.2: |
The van der Pol Equation / 12.3: |
A Hopf Bifurcation / 12.4: |
Exploration: Neurodynamics / 12.5: |
Applications in Mechanics / Chapter 13: |
Newton's Second Law / 13.1: |
Conservative Systems / 13.2: |
Central Force Fields / 13.3: |
The Newtonian Central Force System / 13.4: |
Kepler's First Law / 13.5: |
The Two-Body Problem / 13.6: |
Blowing Up the Singularity / 13.7: |
Exploration: Other Central Force Problems / 13.8: |
Exploration: Classical Limits of Quantum Mechanical Systems / 13.9: |
The Lorenz System / Chapter 14: |
Introduction to the Lorenz System / 14.1: |
Elementary Properties of the Lorenz System / 14.2: |
The Lorenz Attractor / 14.3: |
A Model for the Lorenz Attractor / 14.4: |
The Chaotic Attractor / 14.5: |
Exploration: The Rossler Attractor / 14.6: |
Discrete Dynamical Systems / Chapter 15: |
Introduction to Discrete Dynamical Systems / 15.1: |
The Discrete Logistic Model / 15.2: |
Chaos / 15.4: |
Symbolic Dynamics / 15.5: |
The Shift Map / 15.6: |
The Cantor Middle-Thirds Set / 15.7: |
Exploration: Cubic Chaos / 15.8: |
Exploration: The Orbit Diagram / 15.9: |
Homoclinic Phenomena / Chapter 16: |
The Shil'nikov System / 16.1: |
The Horseshoe Map / 16.2: |
The Double Scroll Attractor / 16.3: |
Homoclinic Bifurcations / 16.4: |
Exploration: The Chua Circuit / 16.5: |
Existence and Uniqueness Revisited / Chapter 17: |
Proof of Existence and Uniqueness / 17.1: |
Continuous Dependence on Initial Conditions / 17.3: |
Extending Solutions / 17.4: |
Nonautonomous Systems / 17.5: |
Differentiability of the Flow / 17.6: |
Bibliography |
Index |
Preface |
First-Order Equations / Chapter 1: |
The Simplest Example / 1.1: |
The Logistic Population Model / 1.2: |
Constant Harvesting and Bifurcations / 1.3: |
Periodic Harvesting and Periodic Solutions / 1.4: |