Brusselator with Two Coupled Cells

exd1
Time-dependent behavior of two identical Brusselator cells with mass exchange.


Variables and parameters:

y1,y2:substances in the first cell

y3,y4:substances of the second cell

$\delta_1,\delta_2$:coupling constants

$A=2, \ \ \delta_1=1, \ \ \delta_2=4,$    $\lambda=B$ (bifurcation parameter)


Differential equations:

\begin{displaymath}\dot y_1 & = A - (B+1)y_1 + y^2_1 y_2 + \delta_1(y_3-y_1) \cr\end{displaymath}


\begin{displaymath}\dot y_2 & = By_1 - y^2_1 y_2 + \delta_2 (y_4 - y_2) \cr\end{displaymath}


\begin{displaymath}\dot y_3 & = A - (B+1)y_3 + y^2_3 y_4 - \delta_1 (y_3 - y_1) \cr\end{displaymath}


\begin{displaymath}\dot y_4 & = By_3 - y^2_3 y_4 - \delta_2 (y_4 - y_2)\cr\end{displaymath}




Comments

Figure 1
Two-cells Brusselator, branching diagram y2(0) versus $\lambda$.

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Figure 1