brainpy.neurons.QuaIF

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

Quadratic Integrate-and-Fire neuron model.

Model Descriptions

In contrast to physiologically accurate but computationally expensive neuron models like the Hodgkin–Huxley model, the QIF model [1] seeks only to produce action potential-like patterns and ignores subtleties like gating variables, which play an important role in generating action potentials in a real neuron. However, the QIF model is incredibly easy to implement and compute, and relatively straightforward to study and understand, thus has found ubiquitous use in computational neuroscience.

\[\tau \frac{d V}{d t}=c(V-V_{rest})(V-V_c) + RI(t)\]

where the parameters are taken to be \(c\) =0.07, and \(V_c = -50 mV\) (Latham et al., 2000).

Model Examples

>>> import brainpy as bp
>>>
>>> group = bp.neurons.QuaIF(1,)
>>>
>>> runner = bp.DSRunner(group, monitors=['V'], inputs=('input', 20.))
>>> runner.run(duration=200.)
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.V, 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.
c	.07		Coefficient describes membrane potential update. Larger than 0.
R	1		Membrane resistance.
tau	10	ms	Membrane time constant. Compute by R * C.
tau_ref	0	ms	Refractory period length.

Model Variables

Variables name	Initial Value	Explanation
V	0	Membrane potential.
input	0	External and synaptic input current.
spike	False	Flag to mark whether the neuron is spiking.
refractory	False	Flag to mark whether the neuron is in refractory period.
t_last_spike	-1e7	Last spike time stamp.

References

[1]

P. E. Latham, B.J. Richmond, P. Nelson and S. Nirenberg (2000) Intrinsic dynamics in neuronal networks. I. Theory. J. Neurophysiology 83, pp. 808–827.

__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.
derivative(V, t, I)
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
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.