Faculty of Science

Objectives

To understanding complex behaviours of physical systems, with emphasis on the stability analysis and the investigation of the various routes to chaos. Recent aspects such as chaos control and synchronization of non-linear systems will also be considered.

Contents

Sources and observations of chaos, phase plane techniques, bifurcations, Rossler systems, period doubling, maps, Poincaré section, examples of logistic and other complex mappings, p-cycles, folding and stretching, dynamics of 2D maps, local and global stability, Lyapunov exponents, Henon map, saddle manifolds, homoclinic tangles, basin of attraction, fractals, phase portrait, reconstruction, chaos in nonlinear oscillators, synchronization and chaos controls, applications to: Bose-Einstein Condensation, laser physics, biophysics, electronics (van der Pol circuits), geophysics and solid state physics.