CondNeuGroupLTC

class brainpy.dyn.CondNeuGroupLTC(size, keep_size=False, C=1.0, A=0.001, V_th=0.0, V_initializer=Uniform(min_val=-70, max_val=-60.0, rng=[3949182063 2081860855]), noise=None, method='exp_auto', name=None, mode=None, init_var=True, input_var=True, spk_type=None, **channels)

Base class to model conductance-based neuron group.

The standard formulation for a conductance-based model is given as

\[C_m {dV \over dt} = \sum_jg_j(E - V) + I_{ext}\]

where \(g_j=\bar{g}_{j} M^x N^y\) is the channel conductance, \(E\) is the reversal potential, \(M\) is the activation variable, and \(N\) is the inactivation variable.

\(M\) and \(N\) have the dynamics of

\[{dx \over dt} = \phi_x {x_\infty (V) - x \over \tau_x(V)}\]

where \(x \in [M, N]\), \(\phi_x\) is a temperature-dependent factor, \(x_\infty\) is the steady state, and \(\tau_x\) is the time constant. Equivalently, the above equation can be written as:

\[\frac{d x}{d t}=\phi_{x}\left(\alpha_{x}(1-x)-\beta_{x} x\right)\]

where \(\alpha_{x}\) and \(\beta_{x}\) are rate constants.

New in version 2.1.9: Modeling the conductance-based neuron model.

Parameters:

• size (int, sequence of int) – The network size of this neuron group.

• method (str) – The numerical integration method.

• name (optional, str) – The neuron group name.

clear_input()

Useful for monitoring inputs.

update(x=None)

The function to specify the updating rule.