Effect of weight perturbations on eigen values

Question

I have a dynamical system of coupled differential equations:

$\dot{X}$ = -X + S( AX + BI)

where X = 7x1 vector, A = 7x7 and B = 7x1 vector. S(x) is a nonlinear sigmoid function.

I want to find the trend of how the eigen values (at a given fixed point) change with perturbations in A and B. How can I do this?

Thanks in advance