Internal Dynamics and Zero dynamics calculation of nonlinear MIMO systems

I am having a situation where I can infer the nature of the internal dynamics (in turn, the zero dynamics) of the system graphically. However, I am not able to calculate the mathematical expression associated with it as the equations are very complex and hard to deduce.
Can anyone help me in suggesting a solution where I can solve or get a form of the zero dynamics/Internal dynamics to apply the nonlinear control technique?