QuaIFRef#
- class brainpy.dyn.QuaIFRef(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=-65.0, V_reset=-68.0, V_th=-30.0, V_c=-50.0, c=0.07, R=1.0, tau=10.0, V_initializer=ZeroInit, tau_ref=0.0, ref_var=False, noise=None)[source]#
Quadratic Integrate-and-Fire neuron model.
Model Descriptions
In contrast to physiologically accurate but computationally expensive neuron models like the Hodgkin–Huxley model, the QIF model [1] seeks only to produce action potential-like patterns and ignores subtleties like gating variables, which play an important role in generating action potentials in a real neuron. However, the QIF model is incredibly easy to implement and compute, and relatively straightforward to study and understand, thus has found ubiquitous use in computational neuroscience.
\[\tau \frac{d V}{d t}=c(V-V_{rest})(V-V_c) + RI(t)\]where the parameters are taken to be \(c\) =0.07, and \(V_c = -50 mV\) (Latham et al., 2000).
References
Examples
There is an example usage:
import brainpy as bp neu = bp.dyn.QuaIFRef(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.
c
.07
Coefficient describes membrane potential update. Larger than 0.
R
1
Membrane resistance.
tau
10
ms
Membrane time constant. Compute by R * C.
tau_ref
0
ms
Refractory period length.
Model Variables
Variables name
Initial Value
Explanation
V
0
Membrane potential.
input
0
External and synaptic input current.
spike
False
Flag to mark whether the neuron is spiking.
refractory
False
Flag to mark whether the neuron is in refractory period.
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.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 isTrainingMode
. It can besoft
andhard
. Default issoft
.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
.