Physics 5413 - Chaos and nonlinear dynamics
Overview
Projects
Project assignments are provided in accessible HTML format and in pdf format for printing.
Examples and extra material
Chapter 1 - What is chaos?
- Logistic map: Time evolution
- Comparison of the bifurcation diagrams of the logistic and sine maps
- Logistic map: Bifurcation diagram
- Renormalization of the logistic map
- Lorenz attractor
- Double pendulum
- Driven damped pendulum
- 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, Rayleigh oscillator (Wolfram cdf files, require free Wolfram Player)
Chapter 4 - Three-dimensional state space and chaos
Chapter 5 - Iterated maps
Lyapunov exponent of the logistic map
U-sequences
Gaussian map
Chapter 6 - Quasi-periodicity and chaos
Periodic vs quasiperiodic motion
Sine-circle map: fixed points,
limit cycles,quasiperiodic motion
Arnold tongues
Devil's staircase
Farey tree
Sine-circle map: Chaos
Sine-circle map: Lyapunov exponent
Chapter 7 - Intermittency and crises
Intermittency in the logistic map, and in the
Lorenz model
Mechanism of intermittency
Crisis in the logistic map
Chapter 8 - Fractal dimensions
Coastline of Norway (Map of Europe)
Covering the coastline, fractal dimension
Koch curve, Sierpinski triangle, Sierpinski carpet
Correlation dimensions of chaotic attractors
Multifractal electronic wave function (courtesy Rudolf Roemer)
Percolation applet
Simulation data for the fractal dimension of the critical percolation cluster
Gnuplot
The Web site for plotting program Gnuplot is www.gnuplot.info.