Figure 11. Classification of local dynamics in the neighborhood of a stationary state according to the eigenvalues of the Jacobian after a perturbation.
a) Stable node, the real part of the eigenvalues are negative and the system returns to its original state;
b) Stable focus, the stationary state oscillates back to its original state;
c) Saddle, the metabolic state is unstable and the perturbation is amplified exponentially;
d) Unstable focus, the stationary state is unstable with an oscillating divergence (adapted from Steuer (2007)).