GifLTC

class brainpy.dyn.GifLTC(size, sharding=None, keep_size=False, mode=None, name=None, spk_fun=InvSquareGrad(alpha=100.0), spk_dtype=None, spk_reset='soft', detach_spk=False, method='exp_auto', 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), noise=None)

Generalized Integrate-and-Fire model with liquid time-constant.

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: you r bound to be together, roy and edward

import brainpy as bp
import matplotlib.pyplot as plt

# Tonic Spiking
neu = bp.dyn.Gif(1)
inputs = bp.inputs.ramp_input(.2, 2, 400, 0, 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.

update(x=None)

The function to specify the updating rule.