brainpy.dyn.neurons.AdQuaIF#

class brainpy.dyn.neurons.AdQuaIF(size, V_rest=- 65.0, V_reset=- 68.0, V_th=- 30.0, V_c=- 50.0, a=1.0, b=0.1, c=0.07, tau=10.0, tau_w=10.0, V_initializer=ZeroInit, w_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, mode=NormalMode, name=None)[source]#

Adaptive quadratic integrate-and-fire neuron model.

Model Descriptions

The adaptive quadratic integrate-and-fire neuron model 1 is given by:

\[\begin{split}\begin{aligned} \tau_m \frac{d V}{d t}&=c(V-V_{rest})(V-V_c) - w + I(t), \\ \tau_w \frac{d w}{d t}&=a(V-V_{rest}) - w, \end{aligned}\end{split}\]

once the membrane potential reaches the spike threshold,

\[\begin{split}V \rightarrow V_{reset}, \\ w \rightarrow w+b.\end{split}\]

Model Examples

>>> import brainpy as bp
>>> group = bp.dyn.AdQuaIF(1, )
>>> runner = bp.dyn.DSRunner(group, monitors=['V', 'w'], inputs=('input', 30.))
>>> runner.run(300)
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8)
>>> fig.add_subplot(gs[0, 0])
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.V, ylabel='V')
>>> fig.add_subplot(gs[1, 0])
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.w, ylabel='w', show=True)

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

../../../../_images/brainpy-dyn-neurons-AdQuaIF-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 \(V_{rest}\).

a

1

The sensitivity of the recovery variable \(u\) to the sub-threshold fluctuations of the membrane potential \(v\)

b

.1

The increment of \(w\) produced by a spike.

c

.07

Coefficient describes membrane potential update. Larger than 0.

tau

10

ms

Membrane time constant.

tau_w

10

ms

Time constant of the adaptation current.

Model Variables

Variables name

Initial Value

Explanation

V

0

Membrane potential.

w

0

Adaptation current.

input

0

External and synaptic input current.

spike

False

Flag to mark whether the neuron is spiking.

t_last_spike

-1e7

Last spike time stamp.

References

1

Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons?. IEEE transactions on neural networks, 15(5), 1063-1070.

2

Touboul, Jonathan. “Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons.” SIAM Journal on Applied Mathematics 68, no. 4 (2008): 1045-1079.

__init__(size, V_rest=- 65.0, V_reset=- 68.0, V_th=- 30.0, V_c=- 50.0, a=1.0, b=0.1, c=0.07, tau=10.0, tau_w=10.0, V_initializer=ZeroInit, w_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, mode=NormalMode, name=None)[source]#

Methods

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

clear_input()

Function to clear inputs in the neuron group.

dV(V, t, w, I_ext)

dw(w, t, V)

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

derivative

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.