17.4 The Jacobian matrix

RevisitingEquation (17.3) we can write our system in matrix form:

\[\begin{equation} \begin{pmatrix} H' \\ L' \end{pmatrix} =\begin{pmatrix} .3 & 0 \\ 0 & -.2 \end{pmatrix} \begin{pmatrix} H \\ L \end{pmatrix} \end{equation}\]

We define the matrix \(\displaystyle J= \begin{pmatrix} .3 & 0 \\ 0 & -.2 \end{pmatrix}\) as the Jacobian matrix. This matrix is key matrix to investigate stability of nonlinear systems.