The general form of a two-chemical reaction-diffusion system is:

$\frac{ \partial a}{\partial t} = F(a,b) + D_a \bigtriangledown^2_a$
$\frac{ \partial b}{\partial t} = F(a,b) + D_b \bigtriangledown^2_b$

where $a,b$ represent the two chemicals,
F(a,b) is the reaction between chemicals a and b,
$D_a, D_b$ are the diffusion rate constants of a and b,
the Laplacian $\bigtriangledown^2_a = \frac{ \partial^2 a}{\partial x^2} + \frac { \partial ^2 a}{\partial y^2}$ is a measure of the concentration of a at one location with respect to it's concentration nearby.