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, method='exp_auto', keep_size=False, 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, method='exp_auto', keep_size=False, name=None)[source]#

Methods

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

dV(V, t, w, I_ext)

dw(w, t, V)

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.

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)

The function to specify the updating rule.

vars([method, level, include_self])

Collect all variables in this node and the children nodes.

Attributes

derivative

global_delay_targets

global_delay_vars

name

steps