Java visualisations for nonlinear dynamics

FitzHugh-Nagumo-model

This applet displays the dynamics of two coupled FitzHugh-Nagumo systems. The FitzHugh-Nagumo system is a prototype model for an excitable, nonlinear, dynamical system.

C++ visualisations for nonlinear dynamics

Odd-Number Limitation

This program simulates the behavior of a subcritical Stuart-Landau oscillator in the uncontrolled case, in case of "delayed feedback control" and "extended delayed feedback control".
The system has an odd Number of Floquet multiplicators. Hence, according to the in 2007 refuted odd-number limitation, a stabilization of the uncotrolled systems unstable limit cycle should be impossible if using the mentioned control methods. The refutation can be reproduced numerically by this program. The results will be visualized to the user by several figures.

Mathematica visualisations for nonlinear dynamics

Rössler Attractor

The chaotic Rössler system can be explored in a three-dimensional visualisation. Its characteristic parameters can be changed using Sliders.

Lorenz Attractor

The parameter of the Lorenz equation can be manipulated while a the consequences are visualized in a spatial or phase plane as well as fourier-spectrum or autot-correlation.

Van der Pol Oszillator

The oscillating VdP-oscillator is found in an closed, serial circuit with a capacitor, an inductor and a nonlinear resistor. It is a clasical non-konservative system with a stable limit cycle.

Logistic Map

Despite it's simple equations the logistic map allready shows many chaotic properties possesing only one parameter for manipulation. Here you can abserve the iteration in three different plots and explore the behaviour by manipulating the starting position and the free paramter.

Hindmarsh-Rose model

The bifurcations of the two-dimensional Hindmarsh-Rose model can be investigated with the help of this applet. A detailed discussion of the model can be found in: Dynamical Systems in Neuroscience.

Note: Open the demonstrations with the free Mathematica CDF Player (Win,Mac,Linux) or Wolfram Mathematica (version 6 or higher).

External resources for the nonlinear dynamics

DynamicSolver - Tool

This free software package can visualize trajectories and trajectorie bundles of abritrary, self defined differential equations in three dimensions, generated from a parameter series.

• Homepage

• Tutorial

The Dynamics Solver tool can also be utilised on Linux, BSD or Mac OS X. Please use the wine programme to do so.

• The double pendulum
• 3-body problem
• chaotic oscillator
• chaotic laser