nnmt.linear_stability._solve_chareq_lambertw_constant_delay

nnmt.linear_stability._solve_chareq_lambertw_constant_delay(branch_nr, tau, delay, connectivity)

Calcs the most critical eigenvalue for neural networks with constant delay.

Uses the Lambert W function to solve the characteristic equation for the respective system. This function can be applied to networks without (Eq. 1 in Helias et al. [2013]) and with (Eq. 1 in Senk et al. [2020]) a spatially structured connectivity. It computes the most critical temporal eigenvalue given by Eq. 8 in Helias et al. [2013] or Eq. 7 in Senk et al. [2020] respectively for any given branch number.

Parameters:

branch_nrint

Branch number.

taunp.array

Time constants in s.

delaynp.array

Delays in s.

connectivitynp.array

Matrix defining the connectivity. For non-spatial networks, this is just the weight matrix. For spatial networks, this is an effective connectivity matrix; each element is the weight multiplied with the Fourier transform of the spatial profile at the wave number k for which the characteristic equation is to be evaluated.

Returns:

eigenvalnp.complex

Temporal eigenvalue solving the characteristic equation.