GifRef

class brainpy.dyn.GifRef(size, sharding=None, keep_size=False, mode=None, spk_fun=InvSquareGrad(alpha=100.0), spk_dtype=None, spk_reset='soft', detach_spk=False, method='exp_auto', name=None, init_var=True, scaling=None, 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), tau_ref=0.0, ref_var=False)

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.

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.

Examples

There is a simple usage:

import brainpy as bp
import matplotlib.pyplot as plt

# Tonic Bursting
neu = bp.dyn.GifRef(1, a=0.005, A1=10., A2=-0.6)
neu.V_th[:] = -50.
inputs = bp.inputs.section_input((1.5, 1.7,), (100, 400))

runner = bp.DSRunner(neu, monitors=['V', 'V_th'])
runner.run(inputs=inputs)

ts = runner.mon.ts

fig, gs = bp.visualize.get_figure(1, 1, 4, 8)
ax1 = fig.add_subplot(gs[0, 0])

ax1.plot(ts, runner.mon.V[:, 0], label='V')
ax1.plot(ts, runner.mon.V_th[:, 0], label='V_th')

plt.show()

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.

Parameters:

• size (TypeVar(Shape, int, Tuple[int, ...])) – int, or sequence of int. The neuronal population size.

• sharding (Union[Sequence[str], Device, Sharding, None]) – The sharding strategy.

• keep_size (bool) – bool. Keep the neuron group size.

• mode (Optional[Mode]) – Mode. The computing mode.

• name (Optional[str]) – str. The group name.

• spk_fun (Callable) – callable. The spike activation function.

• detach_spk (bool) – bool.

• method (str) – str. The numerical integration method.

• spk_type – The spike data type.

• spk_reset (str) – The way to reset the membrane potential when the neuron generates spikes. This parameter only works when the computing mode is TrainingMode. It can be soft and hard. Default is soft.

• tau_ref (Union[float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Callable]) – float, ArrayType, callable. Refractory period length (ms).

• has_ref_var – bool. Whether has the refractory variable. Default is False.

update(x=None)

The function to specify the updating rule.