nnmt.lif.exp._derivative_of_firing_rates_wrt_input_rate¶

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

Derivative of the stationary firing rates with respect to input rate.

See Eq. A.3 in Appendix A of Helias et al. [2013].

Assumptions and approximations:

Diffusion approximation
Linear response approximation
Fast synapses: $\sqrt{\tau_\mathrm{s} / \tau_\mathrm{m}} \ll 1$

Parameters:

mu[float | np.ndarray]: Mean neuron activity in V.
sigma: Standard deviation of neuron activity in V.
tau_m[float | np.ndarray]: Membrane time constant of post-synatic neuron in s.
tau_sfloat: Pre-synaptic time constant in s.
tau_r[float | np.ndarray]: Refractory time in s.
V_th_rel[float | np.ndarray]: Relative threshold potential in V.
V_0_rel[float | np.ndarray]: Relative reset potential in V.
jfloat: Effective connectivity weight in V.

Returns:

float: Unitless derivative.