CSSS 2008 Argentina-Readings: Difference between revisions
From Santa Fe Institute Events Wiki
No edit summary |
No edit summary |
||
| Line 11: | Line 11: | ||
Introduce concepts: state variables, state space, trajectory, initial condition, transient, attractor, basin of attraction, fixed point, stability, bifurcation, parameter | 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. | An extended example: the Lorenz system: history, physical meaning, trajectories, attractors, bifurcations (give examples & reiterate definitions), types of attractors, stability: definition & mathematics, incl. eigen. , un/stable manifolds | ||
Lyapunov exponent and the connection to chaos | Lyapunov exponent and the connection to chaos | ||
Numerical solvers: roles and issues | |||
Shadowing | |||
Projection vs section | |||
Poincare sections in space & time | Poincare sections in space & time | ||
Delay-coordinate embedding | |||
filtering | Examples: roulette, the SFI competition | ||
control of chaos | |||
synchronization & communication | Applications: filtering, control of chaos, synchronization & communication, spacecraft orbits, chaos in the solar system, harnessing the butterfly effect in fluids | ||
spacecraft orbits | |||
chaos in the solar system | |||
harnessing the butterfly effect in fluids | |||
==Week 2== | ==Week 2== | ||
Revision as of 22:22, 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. 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