CSSS 2008 Argentina-Readings
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| CSSS Argentina 2008 |
Week 1
Definition of chaos; examples in various fields
An extended example: the logistic map, in that context, 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 (give examples & reiterate definitions), types of attractors, stability: definition & mathematics, incl. eigenstuff, 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