nnmt.lif.exp._firing_rate_taylor

nnmt.lif.exp._firing_rate_taylor(mu, sigma, V_0_rel, V_th_rel, tau_m, tau_r, tau_s)[source]

Calcs stationary mean firing rates including synaptic filtering.

Calculates the stationary firing rate of a neuron with synaptic filter of time constant tau_s driven by Gaussian noise with mean mu and standard deviation sigma, using Eq. 4.33 in Fourcaud and Brunel [2002] with Taylor expansion around k = \sqrt{\tau_\mathrm{s}/\tau_\mathrm{m}}.

Assumptions and approximations:

  • Diffusion approximation
  • Fast synapses: \sqrt{\tau_\mathrm{s} / \tau_\mathrm{m}} \ll 1
Parameters:
mu[float | np.array]

Mean neuron activity in V.

sigma[float | np.array]

Standard deviation of neuron activity in V.

V_0_rel[float | np.array]

Relative reset potential in V.

V_th_rel[float | np.array]

Relative threshold potential in V.

tau_m[float | 1d array]

Membrane time constant of post-synatic neuron in s.

tau_r[float | 1d array]

Refractory time in s.

tau_sfloat

Pre-synaptic time constant in s.
Returns:
[float | np.array]

Stationary firing rate in Hz.