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12702 Non-linear Dynamics and Chaos - M. ADVANCED PHYSICST, SPE. ASTROPHYSICS

Center

Student Information Service-Master

Departament

Theoretical Physics

Lecturers in charge

Sin datos cargados

Met. Docent

Theoretical questions and problems. A final exam in June.

Met. Avaluació

- -

Bibliografia

G.L. Baker, J.P. Gollub, Chaotic dynamics: an introduction. Cambridge 1996.
D. Kaplan, P. Glass, Understanding nonlinear dynamics. Springer-Verlag 1995.
H. Kantz, T. Shreiber, Nonlinear time series analysis, Cambridge 1997.

Continguts

THEORY PROGRAMME:

1. General view. History.
2. Dynamic systems: general concepts. Examples.
3. Linear systems.
4. Non-linear systems. Asymptotic behaviour: attractors.
5. Routes to chaos.
6. Quantitative characterization of chaotic components.
7. Physical examples: mechanics, circuits, acoustics.
8. From observation to models: non-linear analysis of time series.

PRACTICAL PROGRAMME:

Session-1:
Introduction. Notions associated to non-linearity: Phenomenon of sensitivity to initial conditions, Poincaré section surfaces, power spectrum, fractal dimension, correlation function, attraction basins, bifurcations, Lyapunov exponents.
Session-2:
Practical work on Duffing, Van der Pol, Lorenz, and Hénon-Héiles systems, the properties of which are very well-known.

Session-3:
Debate on how to build a phase space from an experimental signal (or a signal from a numerical simulation): Takens (Sauer) theorem and embedded phase space.

Session-4:
This courseÆs final objective is the non-linear analysis of a time series originating from experimental data. There are a number of situations to choose from.