QuaIFLTC

QuaIFLTC#

class brainpy.dyn.QuaIFLTC(size, sharding=None, keep_size=False, mode=None, name=None, spk_fun=InvSquareGrad(alpha=100.0), spk_dtype=None, spk_reset='soft', detach_spk=False, method='exp_auto', init_var=True, scaling=None, V_rest=-65.0, V_reset=-68.0, V_th=-30.0, V_c=-50.0, c=0.07, R=1.0, tau=10.0, V_initializer=ZeroInit, noise=None)[source]#

Quadratic Integrate-and-Fire neuron model with liquid time-constant.

Model Descriptions

In contrast to physiologically accurate but computationally expensive neuron models like the Hodgkin–Huxley model, the QIF model [1] seeks only to produce action potential-like patterns and ignores subtleties like gating variables, which play an important role in generating action potentials in a real neuron. However, the QIF model is incredibly easy to implement and compute, and relatively straightforward to study and understand, thus has found ubiquitous use in computational neuroscience.

\[\tau \frac{d V}{d t}=c(V-V_{rest})(V-V_c) + RI(t)\]

where the parameters are taken to be \(c\) =0.07, and \(V_c = -50 mV\) (Latham et al., 2000).

References

Examples

Here is an example usage:

import brainpy as bp

neu = bp.dyn.QuaIFLTC(2)

# section input with wiener process
inp1 = bp.inputs.wiener_process(500., n=1, t_start=100., t_end=400.).flatten()
inputs = bp.inputs.section_input([0., 22., 0.], [100., 300., 100.]) + inp1

runner = bp.DSRunner(neu, monitors=['V'])
runner.run(inputs=inputs)

bp.visualize.line_plot(runner.mon['ts'], runner.mon['V'], plot_ids=(0, 1), show=True)

Model Parameters

Parameter	Init Value	Unit	Explanation
V_rest	-65	mV	Resting potential.
V_reset	-68	mV	Reset potential after spike.
V_th	-30	mV	Threshold potential of spike and reset.
V_c	-50	mV	Critical voltage for spike initiation. Must be larger than V_rest.
c	.07		Coefficient describes membrane potential update. Larger than 0.
R	1		Membrane resistance.
tau	10	ms	Membrane time constant. Compute by R * C.
tau_ref	0	ms	Refractory period length.

Model Variables

Variables name	Initial Value	Explanation
V	0	Membrane potential.
input	0	External and synaptic input current.
spike	False	Flag to mark whether the neuron is spiking.
refractory	False	Flag to mark whether the neuron is in refractory period.
t_last_spike	-1e7	Last spike time stamp.

update(x=None)[source]#: The function to specify the updating rule.

QuaIFLTC

Contents

QuaIFLTC#