brainpy.neurons.AdQuaIF

class brainpy.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=None, name=None)

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.neurons.AdQuaIF(1, )
>>> runner = bp.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)

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=None, name=None)

Methods

__init__(size[, V_rest, V_reset, V_th, V_c, ...])
clear_input()	Function to clear inputs in the neuron group.
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
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_state_dict(state_dict[, warn])	Copy parameters and buffers from state_dict into this module and its descendants.
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[, node_cls])
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.
state_dict()	Returns a dictionary containing a whole state of the module.
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
tree_flatten()	Flattens the object as a PyTree.
tree_unflatten(aux, dynamic_values)	New in version 2.3.1.
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	Global delay data, which stores the delay variables and corresponding delay targets.
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.