Thomas Vojta Research Teaching Pegasus Downloads
Missouri S&T Physics Department

Physics 5413 - Chaos, Fractals, and Nonlinear Dynamics


Course description



Due date Project Description Files
Jan 28, 2022 Project 1 Project files
Feb 11, 2022 Project 2 Project files
Feb 25, 2022 Project 3 .
Mar 11, 2022 Project 4a or Project 4b Project 4b files
Mar 25, 2022 Project 5 .
Apr 15, 2022 Project 6 .
Apr 29, 2022 Project 7 .
May 13, 2022 Final Project .

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
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

Lorenz attractor
Saddle cycle
Homoclinic and heteroclinic tangles
Horseshoe map

Chapter 5 - Iterated maps

Lyapunov exponent of the logistic map
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


The Web site for plotting program Gnuplot is