CSSS 2008 Argentina-Readings: Difference between revisions
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==Week 1== | ==Week 1== | ||
Definition of chaos; examples in various fields | |||
An extended example: the logistic map, in that context, introduce: | |||
in that context, introduce: | |||
bifurcations | bifurcations | ||
bifurcation diagram and its structure, incl. Feigenbaum number | bifurcation diagram and its structure, incl. Feigenbaum number | ||
fractals and their connection to chaos | fractals and their connection to chaos | ||
continuous-time dynamics: definition | continuous-time dynamics: definition | ||
Introduce concepts: state variables, state space, trajectory, initial | |||
condition, transient, attractor, basin of attraction, fixed point, stability, bifurcation, parameter | condition, transient, attractor, basin of attraction, fixed point, stability, bifurcation, parameter | ||
An extended example: the Lorenz system | An extended example: the Lorenz system | ||
Revision as of 22:17, 19 October 2008
| 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