Algorithm for the Belousov-Zhabotinsky system

(1)

Initialize variables $N_X$, $N_Y$, $N_Z$, $K_i$ for $i\in{1,\dots,5}$ and $t_{\text{stop}}$.

(2)

Calculate

$$\tilde{K}_i(N_X,N_Y,N_Z)$$

$$\begin{gather*}\begin{split}\pi(N_X,N_Y,N_Z)&=\sum_{j=1}^5\tilde{K}_j p_i(N_X,N_Y,N_Z)&=\frac{\tilde{K}_i}{\pi} \end{split}\end{gather*}$$

where $i\in{1,\dots,5}$.

(3)

Generate

• waiting time
  $\textbf{\textsf{EIV}}(\pi)\longrightarrow\tau$
• reaction index
  $\textbf{\textsf{DIV}}(p_1,\dots,p_5)\longrightarrow\alpha$

(4)

Perform reaction

$$\begin{split} {\text{If }}\alpha&=1{\text{ then}} \begin{ca... ...tarrow N_Y+f/2\\ N_Z\leftarrow N_Z-1 \end{cases} \end{split}$$

(5)

Update time: $t\leftarrow t+\tau$

(6)

If $t<t_{\text{stop}}$ then goto (2).