Dynamical Systems

Course Aim

• Discriminate the linear from the non-linear behavior of any arbitrary system (physical, biological, even social).
• Know how to approach the nonlinear aspects of the system in a principled manner.
• Recognize chaotic behavior (when present) in a given system and analyze it using the available toolkit.
• Approach any arbitrary (for any quantity) time-series and apply a range of analytical tests to extract quantitative information, including but not limited to, Lyapunov exponents, attractor sets, bifurcations, generalized fractal dimensions, correlations etc.

Course Description

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.

Course Contents

Tues and Thurs 0900-1100


weekly assignment and a weekly computer project

Prerequisites or Prior Knowledge

Classical mechanics, e.g. B10

Reference Books

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

Research Specialties