brainpy.neurons.AdQuaIF

class brainpy.neurons.AdQuaIF(*args, input_var=True, spike_fun=None, **kwargs)

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)

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__(*args, input_var=True, spike_fun=None, **kwargs)

Methods

__init__(*args[, input_var, spike_fun])
add_aft_update(key, fun)	Add the after update into this node
add_bef_update(key, fun)	Add the before update into this node
add_inp_fun(key, fun[, label, category])	Add an input function.
clear_input()	Empty function of clearing inputs.
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
dV(V, t, w, I)
dw(w, t, V)
get_aft_update(key)	Get the after update of this node by the given key.
get_batch_shape([batch_size])
get_bef_update(key)	Get the before update of this node by the given key.
get_delay_data(identifier, delay_pos, *indices)	Get delay data according to the provided delay steps.
get_delay_var(name)
get_inp_fun(key)	Get the input function.
get_local_delay(var_name, delay_name)	Get the delay at the given identifier (name).
has_aft_update(key)	Whether this node has the after update of the given key.
has_bef_update(key)	Whether this node has the before update of the given key.
init_param(param[, shape, sharding])	Initialize parameters.
init_variable(var_data, batch_or_mode[, ...])	Initialize variables.
inv_scaling(x[, scale])
jit_step_run(i, *args, **kwargs)	The jitted step function for running.
load_state(state_dict, **kwargs)	Load states from a dictionary.
load_state_dict(state_dict[, warn, compatible])	Copy parameters and buffers from state_dict into this module and its descendants.
nodes([method, level, include_self])	Collect all children nodes.
offset_scaling(x[, bias, scale])
register_delay(identifier, delay_step, ...)	Register delay variable.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables[, var_cls])
register_local_delay(var_name, delay_name[, ...])	Register local relay at the given delay time.
reset(*args, **kwargs)	Reset function which reset the whole variables in the model (including its children models).
reset_local_delays([nodes])	Reset local delay variables.
reset_state([batch_size])
return_info()
save_state(**kwargs)	Save states as a dictionary.
setattr(key, value)	rtype: None
state_dict(**kwargs)	Returns a dictionary containing a whole state of the module.
std_scaling(x[, scale])
step_run(i, *args, **kwargs)	The step run function.
sum_current_inputs(*args[, init, label])	Summarize all current inputs by the defined input functions .current_inputs.
sum_delta_inputs(*args[, init, label])	Summarize all delta inputs by the defined input functions .delta_inputs.
sum_inputs(*args, **kwargs)
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
tracing_variable(name, init, shape[, ...])	Initialize the variable which can be traced during computations and transformations.
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)	Unflatten the data to construct an object of this class.
unique_name([name, type_])	Get the unique name for this object.
update([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

after_updates
before_updates
cur_inputs
current_inputs
delta_inputs
derivative
implicit_nodes
implicit_vars
mode	Mode of the model, which is useful to control the multiple behaviors of the model.
name	Name of the model.
spk_dtype
supported_modes	Supported computing modes.
varshape	The shape of variables in the neuron group.