IF_curr_exp

IF_curr_exp(
    v_rest=-65.0,
    cm=1.0,
    tau_m=20.0,
    tau_refrac=0.0,
    tau_syn_E=5.0,
    tau_syn_I=5.0,
    v_thresh=-50.0,
    v_reset=-65.0,
    i_offset=0.0,
)

Leaky integrate-and-fire model with fixed threshold and decaying-exponential post-synaptic current.

(Separate synaptic currents for excitatory and inhibitory synapses).

The ODEs are solved using the exponential Euler method.

Equivalent code:

IF_curr_exp = Neuron(
    parameters = dict(
        v_rest = ann.Parameter(-65.0),
        cm  = ann.Parameter(1.0),
        tau_m  = ann.Parameter(20.0),
        tau_syn_E = ann.Parameter(5.0),
        tau_syn_I = ann.Parameter(5.0),
        v_thresh = ann.Parameter(-50.0),
        v_reset = ann.Parameter(-65.0),
        i_offset = ann.Parameter(0.0),
    ), 
    equations = [
        ann.Variable(
            'cm * dv/dt = cm/tau_m*(v_rest -v)   + g_exc - g_inh + i_offset',
            method='exponential', init=-65.0
        ),
        ann.Variable('tau_syn_E * dg_exc/dt = - g_exc', method='exponential'),
        ann.Variable('tau_syn_I * dg_inh/dt = - g_inh', method='exponential'),
    ],
    spike = "v > v_thresh",
    reset = "v = v_reset",
    refractory = 0.0
)

Parameters

Name	Type	Description	Default
v_rest	float	Resting membrane potential (mV)	-65.0
cm	float	Capacity of the membrane (nF)	1.0
tau_m	float	Membrane time constant (ms)	20.0
tau_refrac	float	Duration of refractory period (ms)	0.0
tau_syn_E	float	Decay time of excitatory synaptic current (ms)	5.0
tau_syn_I	float	Decay time of inhibitory synaptic current (ms)	5.0
v_thresh	float	Spike threshold (mV)	-50.0
v_reset	float	Reset potential after a spike (mV)	-65.0
i_offset	float	Offset current (nA)	0.0