Demonstration programs for the course of Nonlinear Dynamics and Chaos

 

General Instruction: There are EXE files of Borland C programs. They should work on any Windows computer. To run the program click the moving arrow. To switch off the program click the  X button on your computer. Before starting the program please read the instruction below the title of the program. If the programs does not work in the Web, load the  egavga.bgi and coresponding EXE (by clicking on the moving arrow) files to the same directory on your computer and run the EXE file.

 

1. Chaotic Motion in Periodically Forced Double-Well Oscillator (Duffing oscillator)

Instruction: To run the program click this moving arrow . To switch off the program click the X button on your computer.

 

2. Butterfly Effect in a Chaotic Double Pendulum.

Instruction: To run the program click this moving arrow . To switch off the program click the  X button on your computer. To observe different regimes click 1, 2, and 3 buttons on your computer. This correspond respectively to:

  • Button 1: Two identical double pendulums started at identical initial conditions
  • Button 2: The same as in a previous case, but the pendulums are fixed at the same point.
  • Button 3: The pendulums are started at slightly different initial conditions (the difference is 0.001%).

 

3. Bouncing Ball: Chaotic Motion of a Tennis Ball Reflecting from a Periodically Oscillating Racket. 

Instruction: To run the program click this moving arrow and click the P button on your computer. To switch off the program click the  X button on your computer. You will observe the chaotic motion of the ball and the strange attractor in the coordinates (Phase of the racket, Ball velocity at the moment of reflection). One can change the parameters in the menu (written in Lithuanian). Please switch on the sound when running this program.

 

4. Two Bouncing Balls: The Butterfly Effect.

Instruction: To run the program click this moving arrow and click the P button on your computer. To switch off the program click the  X button on your computer. There are two bouncing balls described in a previous example. The balls are started at slightly different initial conditions (the difference is 0.001%). Please switch on the sound when running this program.