1. a, b, eta are parameters of the equation.
  2. delta is a "small" parameter that sets when a simplified iteration scheme is used that is good only for small values of one of the fields (the scheme is used when the value is less than delta). Increasing delta to 10-2 increases the speed at the cost of faithfulness to the original equations.
  3. amp is the amplitude of a sinusoidal forcing at one corner with frequency 0.5
  4. speed is a benign way of increasing the speed at the cost of jerkiness of the plotting: the iteration is done speed times between each plot update.

The system size is 64 along each edge. The mesh size h for the finite difference code is 0.5 and the time step dt=0.05.

The final frame for the Barkley model shows a state that is disordered in space, but if you run it long enough you can convince yourself that the time dynamics is periodic. In the slightly modified version of the model due to Bar and Eiswirth Phys. Rev. E48 1365 (1993) simulated here the disordered state appears to be more chaotic (see however Strain and Greenside, Phys. Rev. Lett. 80 2306 (1998)).

Last modified Friday, May 7, 1999
Michael Cross