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Stability Analysis
******************

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


.. math::

     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 :math:`F_i` is the ith differential equation and :math:`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()``.