Figure 7

Eigenvalues of the repressilator model. Real (green) and imaginary (red) parts of the eigenvalues λ(β) of $J_f\left(\bar{x}\right)$ of the repressilator model (11) with parameters α=290, n=2, _α0=10 and ${\bar{m}}_i={\bar{p}}_i=12$. The figure was created by calculating the characteristic polynomial χ(λ,β) of $J_f\left(\bar{x}\right)$, which is given here as $\chi (\lambda ,\beta )={(1+\lambda )}^3{(\beta +\lambda )}^3-{\beta }^3{r}^{″}{\left(\bar{p}\right)}^3$ with $r^{″}\left(\bar{x}\right)=\frac{-2\alpha \bar{p}}{{(1+{\bar{p}}^2)}^2}\approx 0.33$, and using a Newton gradient search with several random starting points to find the eigenvalues λwith accuracy $|det(J_f\left(x\right)-\lambda \left(\beta \right)I\left)\right|$<10⁻⁴. Has been created with Additional files 3 and 4.