Dynamical Systems
The course is aimed at the student, scientist, or engineer who wants to learn how to use the ideas in a practical setting. It is developed at a level suitable for beginning graduate students in all fields of science and engineering.
An introduction to chaos theory and related topics in nonlinear dynamics, including the detection and quantification of chaos in experimental data, fractals, and complex systems. Most of the important elementary concepts in nonlinear dynamics are discussed, with emphasis on the physical concepts and useful results rather than mathematical proofs and derivations: there are several other resources for the latter. Courses in Chaos & Nonlinear Dynamics tend to be either purely qualitative or highly mathematical; this course attempts to fill the middle ground by giving the essential equations, but in their simplest possible form.
Week 1 One-dimensional Maps Reading Assignment
Computer Project: Logistic Equation
Week 2 Nonchaotic multi-dimensional flows Assignment
Computer Project: Bifurcation diagrams
Week 3 Dynamical Systems Theory Assignment
Computer Project: Lorenz Attractor
Week 4 Lyapunov Exponents Assignment
Computer Project: Lyapunov exponent
Week 5 Strange Attractors Assignment
Computer Project: Hénon Map
Week 6 Bifurcations Assignment.
Computer Project: Poincaré sections
Week 7 Hamiltonian Chaos Assignment
Computer Project: Chirikov Map
Week 8 Time-series properties Assignment
Computer Project: Autocorrelation function
Week 9 Nonlinear prediction & noise reduction Assignment
Computer Project: Nonlinear prediction
Week 10 Fractals Assignment
Computer Project: State-space reconstruction
Week 11 Calculation of fractal dimension Assignment
Computer Project: Correlation dimension
Week 12 Non-chaotic fractal sets Assignment
Computer Project: Iterated function systems
Time permitting Nonchaotic fractal sets
Spatiotemporal chaos and complexity
weekly assignment and a weekly computer project
Classical mechanics, e.g. B10
Chaos and Nonlinear Dynamics: An introduction to scientists and engineers by R. C. Hilborn (2edn) Oxford, 2000
Chaos in Dynamical Systems by Edward Ott. Cambridge University Press, 2002
Alternate years course, AY2023