Help Using PySindy to solve for a complex (imaginary) equation

[sagastra]

Hi Everyone,

I am trying to fit coefficients to the following equation where I observe the real part of z:

dz/dt = a z^5 + b z^3 + c z + i w z

I understand I can use an odd polynomial basis to solve for a, b, and c, but I am confused what to do with the iwz term, and would like to fit for w if possible. Does anyone know of an example or an idea how to do this. I tried the fourier and cosine basis but maybe used them incorrectly. Any help would be greatly appreciated,
thanks
Amrit