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:

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

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 the command:

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 instead the related method, getReducedJacobian().

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