Barkley's model of an excitable medium
Consider two-variable system of reaction - diffusion equations 
∂u/∂t = (1/ε) u(1 - u)(u - uth )
+ Δu ,
∂v/∂t = u - v ,
uth = (v - b)/a .
The local dynamics (in the absence of diffusion) is illustrated in Fig.1.
u = v = 0 is the stable fixed point. For u > uth
the variable u (the red curve) switches quickly to 1.
Due to the small parameter ε it is fast in comparison to
the recovery variable v (the green curve) which grows exponentially.
When uth = (v + b)/a exceeds u the excitation is
quenched to 0 and v decays exponentially.
In order to take large time steps a semi-implicit integration scheme is
On 2D plane the u values are displayed by the red color
and the v values by the green one. Diffusion propagates excitation
through the plane and we get nonlinear waves.
In this script a = 0.5, b = 0.04, ε = 0.02.
As since 8 bit floating point values (in RGBA textures) are not enough,
therefore floating numbers are stored broken in two cells (bytes).
 Dwight Barkley
"A model for fast computer simulation of waves in excitable media"
Physica D 49 (1991) 61-70
 M.Dowle, R.M.Mantel and D.Barkley
"Fast simulations of waves in three-dimensional excitable media"
Int. Journal of Bifurcation and Chaos, Vol. 7, No. 11 (1997) 2529-2545
Simulations on GPU
updated 14 July 2010