CSSS 2008 Argentina-Readings
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| CSSS Argentina 2008 |
Week 1 (tentative)
Elizabeth Bradley (Nonlinear dynamics)
Definition of chaos; examples in various fields
An extended example: the logistic map. Introduce: bifurcations; bifurcation diagram and its structure, incl. Feigenbaum number; fractals and their connection to chaos
Continuous-time dynamics: definition
Introduce concepts: state variables, state space, trajectory, initial condition, transient, attractor, basin of attraction, fixed point, stability, bifurcation, parameter
An extended example: the Lorenz system: history, physical meaning, trajectories, attractors, bifurcations (examples & definitions), types of attractors, stability: definition & mathematics, eigen. , un/stable manifolds, Lyapunov exponent and the connection to chaos
Numerical solvers: roles and issues
Shadowing
Projection vs section
Poincare sections in space & time
Delay-coordinate embedding
Examples: roulette, the SFI competition
Applications: filtering, control of chaos, synchronization & communication, spacecraft orbits, chaos in the solar system, harnessing the butterfly effect in fluids