Stabilization of different fixed points for an artificial gene regulatory network.

<p>Upper left panel: the control is modulated so as to enhance the activity of the peripheral nodes of the tree, as compared to the inner ones. Upper right panel: the control makes now the bulk nodes more active as compared to the peripheral ones. Lower panel: the root locus diagram relative to the situation displayed in the second panel is plotted. Blue circles stand for the position of the complex eigenvalues when <i>ρ</i> = 0, while green crosses identify the eigenvalue obtained for <i>ρ</i> → ∞. The vertical red line represents the asymptote that attracts two of the modified eigenvalues, when <i>ρ</i> → ∞. The red dots show the computed spectrum, calculated when increasing <i>ρ</i>. In this case the matrix <b><i>A</i></b> contains an identical number of ±1 entries. These are randomly assigned and kept unchanged for all tests performed. The figure on the right is a zoom of the plot displayed on the left.