WOB Examples

Three Coupled Cells with Brusselator Reaction

exa1

Variables and parameters:

y₁,y₂: substances in the first cell

y₃,y₄: substances in the second cell

y₅,y₆: substances in the third cell

$\lambda$ : coupling coefficient (bifurcation parameter)

System of equations:

$\begin{displaymath}2 - 7 y_1 + y^2_1 y_2 + \lambda (y_3 -y_1) & = 0 \cr \end{displaymath}$

$\begin{displaymath}6 y_1 - y^2_1 y_2 + 10\lambda (y_4 -y_2) & = 0 \cr \end{displaymath}$

$\begin{displaymath}2 - 7 y_3 + y^2_3 y_4 + \lambda (y_1 +y_5 -2y_3 ) & = 0 \cr \end{displaymath}$

$\begin{displaymath}6 y_3 - y^2_3 y_4 + 10\lambda (y_2 +y_6 -2 y_4 )& = 0 \cr \end{displaymath}$

$\begin{displaymath}2 - 7 y_5 + y^2_5 y_6 + \lambda (y_3 -y_5) & = 0 \cr \end{displaymath}$

$\begin{displaymath}6 y_5 - y^2_5 y_6 + 10\lambda (y_4 -y_6) & = 0 \cr \end{displaymath}$

Figure 1
Bifurcation diagram y₁ versus $\lambda$ .

Figure 2
y₁ versus $\lambda$ , detail of Figure 1.

Figure 3
Schematic bifurcation; for numbers of bifurcations see Table.