MAM2046W — Nonlinear Dynamics

MAM2046W — Second Year Nonlinear Dynamics

Course notes based on Strogatz's Nonlinear Dynamics and Chaos, University of Cape Town.

Textbook: Nonlinear Dynamics and Chaos by Steven H. Strogatz.

Chapter 0: Introduction

Section 0.0: Course Introduction

Chapter 1: Two-Dimensional Nonlinear Systems

Section 1.1: Phase portraits in two dimensions
Section 1.2: Existence and Uniqueness
Section 1.3: Fixed Points and Linearisation
Section 1.4: Conservative systems
Section 1.5: Reversible systems
Section 1.6: Index Theory

Chapter 2: Limit Cycles

Section 2.1: Limit Cycles
Section 2.2: Ruling out closed orbits
Section 2.3: The Poincaré-Bendixson theorem
Section 2.4: Liénard Systems
Section 2.5: Relaxation oscillations
Section 2.6: Weakly nonlinear oscillators

Chapter 3: Bifurcations

Section 3.1: Saddle-nodes, transcritical and pitchfork bifurcations in two dimensions
Section 3.2: Hopf bifurcations
Section 3.3: Oscillating chemical reactions
Section 3.4: Global bifurcations of cycles
Section 3.5: Coupled oscillators and quasiperiodicity
Section 3.6: Poincaré maps

Chapter 4: Chaos

Section 4.1: The Lorenz equations
Lorenz Equations (Continued)
Section 4.2: The Lorenz equations - detecting chaos

MAM2046W · University of Cape Town · Based on Strogatz's Nonlinear Dynamics and Chaos

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