I have a set of four non-linear ODEs representing a negative feedback. I have done parameter variation by random sampling to study the sensitivity of steady state and other dynamic properties to parameter fluctuations.From the analytical expressions of steady state I have calculated jacobian and its eigenvalues for each parameter set and based on that I could observe the fraction of oscillating cases (complex eigenvalues). I wish to calculate something like damping factor for these cases. I am not sure what to use as a metric. I think of three choices:Least eigenvalue (absolute value of the real part). This would be rate limiting.Biggest eigenvalue (absolute value of the real part). This might dictate the initial damping (which is what I am basically interested in).Determinant of the jacobian (?)Please suggest me what is the right metric or let me know if there are better alternatives.
Damping factor for a set of non-linear ODEs
jacobian;oscillations