CSSS 2008 Argentina-Readings: Difference between revisions
From Santa Fe Institute Events Wiki
No edit summary |
No edit summary |
||
| Line 4: | Line 4: | ||
definition of chaos; examples in various fields | definition of chaos; examples in various fields | ||
an extended example: the logistic map | 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 | |||
==Week 2== | ==Week 2== | ||
Revision as of 22:16, 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