# 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))[source]#

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

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

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.
reset_state(batch_size=None, **kwargs)[source]#

Reset function which resets local states in this model.

Simply speaking, this function should implement the logic of resetting of local variables in this node.

update(x=None)[source]#

The function to specify the updating rule.