'Chaos: an
introduction to dynamical systems',
K. T. Alligood, T. D. Sauer,
J.A. Yorke, Springer, 2000.
'Nonlinear dynamics and chaos',
S. Strogatz, Westview press, 2000.
-
I. Discrete dynamical systems: nonlinear phenomena and the logistic map (Alligood, chap. 1).
- II. Henon map, restricted three-body problem, saddle points (Alligood, chap 2)
- III. Phase portraits around equilibria
(linear/nonlinear, discrete/continuous, classification of equilibria,
Lyapunov exponents (Alligood, chap 2, Strogatz)
- IV. Bistability and hysteresis. Saddle-node bifurcation. Examples.
- V. Gradient systems. Lyapunov stability.
- VI. Conservative systems, damping, pendulum equation, Duffing oscillator.
- VII.
Limit cycles. Van der Pol oscillator. Poincare-Bendixon theorem
- VIII. Limit cycles. Weakly nonlinear oscillators and relaxation oscillators
- IX. Limit sets. LaSalle Invariance Principle. Convergence issues.
- X Bifurcations of points and cycles.
- XI. Chaos
in differential equations. Lorenz model.
- XII. Strange attractors
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Références et
transparents
- Références additionnelles:
- 'Spikes, decisions, and actions. Dynamical
foundations of neuroscience', H.R. Wilson, Oxford University Press,
1999.
- 'Nonlinear Oscillations, Dynamical Systems, and
Bifurcation of Vector Fields', Guckenheimer, Holmes, Springer-Verlag,
1983.
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Evaluation
- Devoirs individuels a
remettre pendant le semestre
- Un
travail individuel et présentation orale d'un rapport écrit pour
l'examen
Les informations relatives au projet et les
différents sujets proposés peuvent être consultés
ICI
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