AdQuaIFLTC#
- class brainpy.dyn.AdQuaIFLTC(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=-65.0, V_reset=-68.0, V_th=-30.0, V_c=-50.0, a=1.0, b=0.1, c=0.07, tau=10.0, tau_w=10.0, V_initializer=ZeroInit, w_initializer=ZeroInit, noise=None)[source]#
Adaptive quadratic integrate-and-fire neuron model with liquid time-constant.
Model Descriptions
The adaptive quadratic integrate-and-fire neuron model [1] is given by:
\[\begin{split}\begin{aligned} \tau_m \frac{d V}{d t}&=c(V-V_{rest})(V-V_c) - w + I(t), \\ \tau_w \frac{d w}{d t}&=a(V-V_{rest}) - w, \end{aligned}\end{split}\]once the membrane potential reaches the spike threshold,
\[\begin{split}V \rightarrow V_{reset}, \\ w \rightarrow w+b.\end{split}\]References
Examples
Here is an example usage:
import brainpy as bp neu = bp.dyn.AdQuaIFLTC(2) # section input with wiener process inp1 = bp.inputs.wiener_process(500., n=1, t_start=100., t_end=400.).flatten() inputs = bp.inputs.section_input([0., 22., 0.], [100., 300., 100.]) + inp1 runner = bp.DSRunner(neu, monitors=['V']) runner.run(inputs=inputs) bp.visualize.line_plot(runner.mon['ts'], runner.mon['V'], plot_ids=(0, 1), show=True)
Model Parameters
Parameter
Init Value
Unit
Explanation
V_rest
-65
mV
Resting potential.
V_reset
-68
mV
Reset potential after spike.
V_th
-30
mV
Threshold potential of spike and reset.
V_c
-50
mV
Critical voltage for spike initiation. Must be larger than \(V_{rest}\).
a
1
The sensitivity of the recovery variable \(u\) to the sub-threshold fluctuations of the membrane potential \(v\)
b
.1
The increment of \(w\) produced by a spike.
c
.07
Coefficient describes membrane potential update. Larger than 0.
tau
10
ms
Membrane time constant.
tau_w
10
ms
Time constant of the adaptation current.
Model Variables
Variables name
Initial Value
Explanation
V
0
Membrane potential.
w
0
Adaptation current.
input
0
External and synaptic input current.
spike
False
Flag to mark whether the neuron is spiking.
t_last_spike
-1e7
Last spike time stamp.