Brusselator

The Brusselator models the concentration of two chemicals $U$ and $V$ characterized by the reactions

\begin{align*} A & \rightarrow U \\ 2U + V & \rightarrow 3U \\ B + U & \rightarrow V + C \\ U & \rightarrow D \; . \end{align*}

The simulation shows the concentration of $U$ through time, under the assumptions that $A$ and $B$ are in large excess and that $U$ and $V$ diffuse in different ways.

Some parameters values that you can try out: , , .

2.300

0.010

25.000

0.020

Under the assumptions mentioned above, the concentrations of $U$ and $V$ are described by two partial differential equations

\begin{align*} \frac{\partial u}{\partial t} & = D_{0} \nabla^2 u + a - (1 - b) u + v u^2 \\ \frac{\partial v}{\partial t} & = D_{1} \nabla^2 v + b u - v u^2 \; , \end{align*}

where $a$ , $b$ , $D_0$ and $D_1$ are parameters of the model, and the concentration of a chemical is denoted by its lower case letter. The simulation starts with a configuration where $u_0(x,y)=a+\xi_u(x,y)$ and $v_0(x,y)=b/a+\xi_v(x,y)$ , with $\xi_u(x,y)$ and $\xi_v(x,y)$ small perturbations.