brainpy.dyn.neurons.QuaIF

class brainpy.dyn.neurons.QuaIF(size, 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, tau_ref=0.0, V_initializer=ZeroInit, keep_size=False, method='exp_auto', name=None)

Quadratic Integrate-and-Fire neuron model.

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).

Model Examples

>>> import brainpy as bp
>>>
>>> group = bp.dyn.QuaIF(1,)
>>>
>>> runner = bp.dyn.DSRunner(group, monitors=['V'], inputs=('input', 20.))
>>> runner.run(duration=200.)
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.V, show=True)

(Source code, png, hires.png, pdf)

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.

References

1

P. E. Latham, B.J. Richmond, P. Nelson and S. Nirenberg (2000) Intrinsic dynamics in neuronal networks. I. Theory. J. Neurophysiology 83, pp. 808–827.

__init__(size, 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, tau_ref=0.0, V_initializer=ZeroInit, keep_size=False, method='exp_auto', name=None)

Methods

__init__(size[, V_rest, V_reset, V_th, V_c, ...])
derivative(V, t, I_ext)
get_delay_data(name, delay_step, *indices)	Get delay data according to the provided delay steps.
ints([method])	Collect all integrators in this node and the children nodes.
load_states(filename[, verbose])	Load the model states.
nodes([method, level, include_self])	Collect all children nodes.
register_delay(name, delay_step, delay_target)	Register delay variable.
register_implicit_nodes(nodes)
register_implicit_vars(variables)
reset()	Reset function which reset the whole variables in the model.
reset_delay(name, delay_target)	Reset the delay variable.
save_states(filename[, variables])	Save the model states.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
unique_name([name, type_])	Get the unique name for this object.
update(t, dt, **kwargs)	The function to specify the updating rule.
update_delay(name, delay_data)	Update the delay according to the delay data.
vars([method, level, include_self])	Collect all variables in this node and the children nodes.

Attributes

global_delay_vars
name
steps