brainpy.neurons.GIF

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

Generalized Integrate-and-Fire model.

Model Descriptions

The generalized integrate-and-fire model [1] is given by

\[ \begin{align}\begin{aligned}&\frac{d I_j}{d t} = - k_j I_j\\&\frac{d V}{d t} = ( - (V - V_{rest}) + R\sum_{j}I_j + RI) / \tau\\&\frac{d V_{th}}{d t} = a(V - V_{rest}) - b(V_{th} - V_{th\infty})\end{aligned}\end{align} \]

When \(V\) meet \(V_{th}\), Generalized IF neuron fires:

\[ \begin{align}\begin{aligned}&I_j \leftarrow R_j I_j + A_j\\&V \leftarrow V_{reset}\\&V_{th} \leftarrow max(V_{th_{reset}}, V_{th})\end{aligned}\end{align} \]

Note that \(I_j\) refers to arbitrary number of internal currents.

Model Examples

• Detailed examples to reproduce different firing patterns

Model Parameters

Parameter	Init Value	Unit	Explanation
V_rest	-70	mV	Resting potential.
V_reset	-70	mV	Reset potential after spike.
V_th_inf	-50	mV	Target value of threshold potential \(V_{th}\) updating.
V_th_reset	-60	mV	Free parameter, should be larger than \(V_{reset}\).
R	20		Membrane resistance.
tau	20	ms	Membrane time constant. Compute by \(R * C\).
a	0		Coefficient describes the dependence of \(V_{th}\) on membrane potential.
b	0.01		Coefficient describes \(V_{th}\) update.
k1	0.2		Constant pf \(I1\).
k2	0.02		Constant of \(I2\).
R1	0		Free parameter. Describes dependence of \(I_1\) reset value on \(I_1\) value before spiking.
R2	1		Free parameter. Describes dependence of \(I_2\) reset value on \(I_2\) value before spiking.
A1	0		Free parameter.
A2	0		Free parameter.

Model Variables

Variables name	Initial Value	Explanation
V	-70	Membrane potential.
input	0	External and synaptic input current.
spike	False	Flag to mark whether the neuron is spiking.
V_th	-50	Spiking threshold potential.
I1	0	Internal current 1.
I2	0	Internal current 2.
t_last_spike	-1e7	Last spike time stamp.

References

[1]

Mihalaş, Ştefan, and Ernst Niebur. “A generalized linear integrate-and-fire neural model produces diverse spiking behaviors.” Neural computation 21.3 (2009): 704-718.

[2]

Teeter, Corinne, Ramakrishnan Iyer, Vilas Menon, Nathan Gouwens, David Feng, Jim Berg, Aaron Szafer et al. “Generalized leaky integrate-and-fire models classify multiple neuron types.” Nature communications 9, no. 1 (2018): 1-15.

__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.
dI1(I1, t)
dI2(I2, t)
dV(V, t, I1, I2, I)
dVth(V_th, 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.