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=None, V_initializer=ZeroInit, noise=None, keep_size=False, mode=NormalMode, method='exp_auto', name=None)[source]#

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)

../../../../_images/brainpy-dyn-neurons-QuaIF-1.png

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=None, V_initializer=ZeroInit, noise=None, keep_size=False, mode=NormalMode, method='exp_auto', name=None)[source]#

Methods

__init__(size[, V_rest, V_reset, V_th, V_c, ...])

clear_input()

Function to clear inputs in the neuron group.

derivative(V, t, I_ext)

get_batch_shape([batch_size])

get_delay_data(identifier, delay_step, *indices)

Get delay data according to the provided delay steps.

load_states(filename[, verbose])

Load the model states.

nodes([method, level, include_self])

Collect all children nodes.

offline_fit(target, fit_record)

offline_init()

online_fit(target, fit_record)

online_init()

register_delay(identifier, delay_step, ...)

Register delay variable.

register_implicit_nodes(*nodes, **named_nodes)

register_implicit_vars(*variables, ...)

reset([batch_size])

Reset function which reset the whole variables in the model.

reset_local_delays([nodes])

Reset local delay variables.

reset_state([batch_size])

Reset function which reset the states in the model.

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(tdi[, x])

The function to specify the updating rule.

update_local_delays([nodes])

Update local delay variables.

vars([method, level, include_self])

Collect all variables in this node and the children nodes.

Attributes

global_delay_data

mode

Mode of the model, which is useful to control the multiple behaviors of the model.

name

Name of the model.

varshape

The shape of variables in the neuron group.