IzhikevichRef

IzhikevichRef#

class brainpy.state.IzhikevichRef(in_size, a=Quantity(0.02, "kHz"), b=Quantity(0.2, "kHz"), c=Quantity(-65., "mV"), d=Quantity(8., "mV / ms"), V_th=Quantity(30., "mV"), tau_ref=Quantity(0., "ms"), V_initializer=Constant(value=-65. mV), u_initializer=Constant(value=0. mV / ms), spk_fun=ReluGrad(alpha=0.3, width=1.0), spk_reset='hard', ref_var=False, name=None)#

Izhikevich neuron model with refractory period.

This class implements the Izhikevich neuron model with an absolute refractory period. During the refractory period after a spike, the neuron cannot fire regardless of input, which better captures the behavior of biological neurons that exhibit a recovery period after action potential generation.

The model is characterized by the following equations:

When not in refractory period:

\[ \frac{dV}{dt} = 0.04 V^2 + 5V + 140 - u + I(t) \]

\[ \frac{du}{dt} = a(bV - u) \]

During refractory period:

\[ V = c, \quad u = u \]

Spike condition: If \(V \geq V_{th}\) and not in refractory period: emit spike, set \(V = c\), \(u = u + d\), and enter refractory period for \(\tau_{ref}\)

Parameters:

  • in_size (Size) – Size of the input to the neuron.

  • a (ArrayLike, default 0.02 / u.ms) – Time scale of the recovery variable u.

  • b (ArrayLike, default 0.2 / u.ms) – Sensitivity of the recovery variable u to the membrane potential V.

  • c (ArrayLike, default -65. * u.mV) – After-spike reset value of the membrane potential.

  • d (ArrayLike, default 8. * u.mV / u.ms) – After-spike increment of the recovery variable u.

  • V_th (ArrayLike, default 30. * u.mV) – Spike threshold voltage.

  • tau_ref (ArrayLike, default 0. * u.ms) – Refractory period duration.

  • V_initializer (Callable) – Initializer for the membrane potential state.

  • u_initializer (Callable) – Initializer for the recovery variable state.

  • spk_fun (Callable, default surrogate.ReluGrad()) – Surrogate gradient function for the non-differentiable spike generation.

  • spk_reset (str, default 'hard') – Reset mechanism after spike generation.

  • ref_var (bool, default False) – Whether to expose a boolean refractory state variable.

  • name (str, optional) – Name of the neuron layer.

V#

Membrane potential.

Type:

HiddenState

u#

Recovery variable.

Type:

HiddenState

last_spike_time#

Time of the last spike, used to implement refractory period.

Type:

ShortTermState

refractory#

Neuron refractory state (if ref_var=True).

Type:

HiddenState

See also

Izhikevich

Izhikevich model without refractory period.

Notes

  • The refractory period is implemented by tracking the time of the last spike and preventing membrane potential updates if the elapsed time is less than tau_ref.

  • During the refractory period, the membrane potential remains at the reset value c regardless of input current strength.

  • Refractory periods prevent high-frequency repetitive firing and are critical for realistic neural dynamics [1].

  • The simulation environment time variable ‘t’ is used to track the refractory state.

  • For parameter selection guidelines, see [2].

References

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an IzhikevichRef neuron layer with 10 neurons
>>> izh_ref = brainpy.state.IzhikevichRef(10, tau_ref=2.*u.ms)
>>> # Initialize the state
>>> izh_ref.init_state(batch_size=1)
>>> # Generate inputs and run simulation
>>> time_steps = 100
>>> inputs = brainstate.random.randn(time_steps, 1, 10) * u.mV / u.ms
>>> with brainstate.environ.context(dt=0.1 * u.ms):
...     for t in range(time_steps):
...         with brainstate.environ.context(t=t*0.1*u.ms):
...             spikes = izh_ref.update(x=inputs[t])
get_spike(V=None)[source]#

Generate spikes based on neuron state variables.

This abstract method must be implemented by subclasses to define the spike generation mechanism. The method should use the surrogate gradient function self.spk_fun to enable gradient-based learning.

Parameters:

  • *args – Positional arguments (typically state variables like membrane potential)

  • **kwargs – Keyword arguments

Returns:

Binary spike tensor where 1 indicates a spike and 0 indicates no spike.

Return type:

ArrayLike

Raises:

NotImplementedError – If the subclass does not implement this method.

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

State initialization function.

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

State resetting function.