Eigenvalues for a system of nonlinear ordinary differential equations

Hello, I'm adapting code from xpp into matlab. Briefly, I have a nonlinear system of ordinary differential equations (the Hodgkin-Huxley model) and I want to compute the eigenvalues under different conditions to get some intuition.

In xpp this is a two-button process. However I'm clueless about how to do this in Matlab (because I'm clueless about how it's actually done). If it were a linear system the e-values would be equal to the e-values of the Jacobian, but since it's nonlinear I'm lost. I'm guessing the solution is necessarily numerical. Can anyone shed some light?

Thanks.

-greg