CONTENTS 2: Flows on the Line 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 3.1 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.
1 Examples and Definitions 4.2 Uniform Oscillator 4.3 Nonuniform Oscillator 4.4 Overdamped Pendulum 4.5 Fireflies 4.6 Superconducting Josephson Junctions 5: Linear Systems 5.1 Definitions and Examples 5.2 Classification of Linear Systems 5.
3 Love Affairs 6 Phase Plane 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 7.1 Examples 7.2 Ruling Out Closed Orbits 7.3 Poincar'e-Bendixson Theorem 7.4 Li'enard Systems 7.5 Relaxation Oscillations 7.6 Weakly Nonlinear Oscillators 8: Bifurcations Revisited 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 Poincar'e Maps 9: Lorenz Equations 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 10.1 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 11.1 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.
1 The Simplest Examples 12.2 H'enon Map 12.3 Rossler System 12.4 Chemical Chaos and Attractor Reconstruction 12.5 Forced Double-Well Oscillator.