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)

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)

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)

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.
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)	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

derivative
global_delay_vars
name
steps