Physics 355 - Chaos and Nonlinear Dynamics
Overview
Projects
| Due date | Project Description | Files |
|---|---|---|
| Jan 25, 2008 | Project 1 | Project files |
| Feb 8, 2008 | Project 2 | Project files |
| Feb 22, 2008 | Project 3 | . |
| Mar 7, 2008 | Project 4 | . |
| Mar 21, 2008 | Project 5 | Project files |
| April 11, 2008 | Project 6 | . |
| April 25, 2008 | Project 7 | . |
| Final's week | Project 8 | . |
Examples and extra material
Chapter 1 - What is chaos?
Logistic map: Time evolution
Logistic map: Bifurcation diagram
Comparison of the bifurcation diagrams of the logistic and sine maps
Renormalization of the logistic map
Lorenz attractor
Double pendulum
Pendulum Lab by Franz-Josef Elmer, University of Basel, Switzerland
Bifurcation diagram of driven damped pendulum
Chapter 3 - Dynamics in state space
Chemical oscillations, part of the IDEA project at Washington State Univ.
Van der Pol oscillator, part of the Vibe oscillator simulator,
see also here
Chapter 4 - 3D state space + chaos
Saddle cycles
Homoclinic and heteroclinic tangles
Horseshoe map
Michael Cross' Lorenz applet
Chapter 5 - Iterated maps
Logistic map
Logistic map iterated twice
Logistic map iterated four times
Lyapunov exponent of logistic map
Chapter 6 - Quasiperiodicity and chaos
Periodic vs quasiperiodic motion
Fixed points of the sine-circle map
Limit cycles of the sine-circle map
Quasiperiodic trajectory in the sine-circle map
Chapter 8 - Fractals and Multifractals
Koch snowflake
Sierpinski Triangle
Sierpinski Carpet
Percolation applet
Fractality of infinite percolation cluster
Multifractal electronic wave function (courtesy R. Roemer)
DLA applet by Chi-Hang Lam
Copper sulfate DLA cluster
Chapter 10 - Quantum Chaos
Gnuplot
The Web site for plotting program Gnuplot is www.gnuplot.info.
The Windows executable can be found here.