LifRefLTC

class brainpy.dyn.LifRefLTC(size, sharding=None, keep_size=False, mode=None, spk_fun=InvSquareGrad(alpha=100.0), spk_dtype=None, detach_spk=False, spk_reset='soft', method='exp_auto', name=None, init_var=True, scaling=None, V_rest=0.0, V_reset=-5.0, V_th=20.0, R=1.0, tau=10.0, V_initializer=ZeroInit, tau_ref=0.0, ref_var=False, noise=None)

Leaky integrate-and-fire neuron model with liquid time-constant which has refractory periods .

The formal equations of a LIF model [1] is given by:

\[\begin{split}\tau \frac{dV}{dt} = - (V(t) - V_{rest}) + RI(t) \\ \text{after} \quad V(t) \gt V_{th}, V(t) = V_{reset} \quad \text{last} \quad \tau_{ref} \quad \text{ms}\end{split}\]

where \(V\) is the membrane potential, \(V_{rest}\) is the resting membrane potential, \(V_{reset}\) is the reset membrane potential, \(V_{th}\) is the spike threshold, \(\tau\) is the time constant, \(\tau_{ref}\) is the refractory time period, and \(I\) is the time-variant synaptic inputs.

[1]

Abbott, Larry F. “Lapicque’s introduction of the integrate-and-fire model neuron (1907).” Brain research bulletin 50, no. 5-6 (1999): 303-304.

Examples

There is an example usage:

import brainpy as bp

neu = bp.dyn.LifRefLTC(1, )


# example for section input
inputs = bp.inputs.section_input([0., 21., 0.], [100., 300., 100.])

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

bp.visualize.line_plot(runner.mon['ts'], runner.mon['V'], show=True)

Parameters:

• V_rest (Union[float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Callable]) – float, ArrayType, callable. Resting membrane potential.

• V_reset (Union[float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Callable]) – float, ArrayType, callable. Reset potential after spike.

• V_th (Union[float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Callable]) – float, ArrayType, callable. Threshold potential of spike.

• R (Union[float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Callable]) – float, ArrayType, callable. Membrane resistance.

• tau (Union[float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Callable]) – float, ArrayType, callable. Membrane time constant.

• V_initializer (Union[Callable, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray)]) – ArrayType, callable. The initializer of membrane potential.

• 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.