620-341 Dynamical Systems and Chaos

Note

Students may only gain credit for one of 620-341, 618-341 (1997 Handbook).

Credit Points

Coordinator

Prerequisites

620-130 or 620-132 (1997 Handbook 618-130 or 618-132), and either one of 620-201, 620-231, 620-232, 620-252 or one of the 1997 Handbook subjects 618-201, 618-231, 618-232, 618-252.

Semester

Contact

Subject Description

Students completing this subject should comprehend

• the basic concepts and recent developments in the fields of dynamical systems and chaos, including stability of equilibria and renormalisation theory of transitions to chaos;

have developed the ability to

• analyse simple nonlinear discrete and continuous dynamical systems, and to chart parameter regions of stability, periodicity and chaos;

and appreciate

• the power as well as the limitations of dynamical systems theory and chaos applied to realistic complex systems.

Dynamical systems: phase space, Poincare sections, phase portraits, invariant measures. Chaos: integrable and chaotic systems, maps on an interval, period doubling and universality, iteration in the complex plane, Mandelbrot and Julia sets, renormalisation and scaling, reversible mappings, KAM theorems, strange attractors, fractals, limit cycles, Hopf bifurcation, Lorentz attractor, Lyapunov exponents, dimensions of strange attractors, hierarchies of chaos; applications to ecology, chemical reactions, economics, management and meteorology.

Assessment

Up to 24 pages of written assignments and a three-hour end-of-semester written examination.