Stability Analysis

The stability of a biochemical system is determined by the eigenvalues of the Jacobian matrix. Given m floating species and n reactions, the Jacobian matrix is defined as follows:

J=\begin{bmatrix} \dfrac{\partial F_1}{\partial S_1} & \cdots & \dfrac{\partial F_1}{\partial S_m} \\
\vdots & \ddots & \vdots \\ \dfrac{\partial F_n}{\partial S_1} & \cdots & \dfrac{\partial F_n}{\partial S_m}

where F_i is the ith differential equation and S_i the ith floating species. From RoadRunner it is easy to obtain the Jacobian matrix using :cpp:rr::RoadRunner::getFullJacobian, i.e.:

Jac = rr.getFullJacobian()

which returns the Jacobian matrix in the variable Jac.

It is possible for full Jacobian to be singular. In these situations one should call the related method, rr::RoadRunner::getReducedJacobian().