brainpy.neurons.GIF

class brainpy.neurons.GIF(size, V_rest=-70.0, V_reset=-70.0, V_th_inf=-50.0, V_th_reset=-60.0, R=20.0, tau=20.0, a=0.0, b=0.01, k1=0.2, k2=0.02, R1=0.0, R2=1.0, A1=0.0, A2=0.0, V_initializer=OneInit(value=-70.0), I1_initializer=ZeroInit, I2_initializer=ZeroInit, Vth_initializer=OneInit(value=-50.0), noise=None, method='exp_auto', keep_size=False, input_var=True, name=None, mode=None, spike_fun=<brainpy._src.math.surrogate._utils.VJPCustom object>)

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__(size, V_rest=-70.0, V_reset=-70.0, V_th_inf=-50.0, V_th_reset=-60.0, R=20.0, tau=20.0, a=0.0, b=0.01, k1=0.2, k2=0.02, R1=0.0, R2=1.0, A1=0.0, A2=0.0, V_initializer=OneInit(value=-70.0), I1_initializer=ZeroInit, I2_initializer=ZeroInit, Vth_initializer=OneInit(value=-50.0), noise=None, method='exp_auto', keep_size=False, input_var=True, name=None, mode=None, spike_fun=<brainpy._src.math.surrogate._utils.VJPCustom object>)

Methods

__init__(size[, V_rest, V_reset, V_th_inf, ...])
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.
dI1(I1, t)
dI2(I2, t)
dV(V, t, I1, I2, I_ext)
dVth(V_th, 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, compatible])	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.
register_delay(identifier, delay_step, ...)	Register delay variable.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables[, var_cls])
reset(*args, **kwargs)	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)	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

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.