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Izhikevich

Izhikevich#

class brainpy.dyn.Izhikevich(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_th=30.0, p1=0.04, p2=5.0, p3=140.0, a=0.02, b=0.2, c=-65.0, d=8.0, tau=10.0, R=1.0, V_initializer=OneInit(value=-70.0), u_initializer=None, noise=None)[source]#

The Izhikevich neuron model.

Model Descriptions

The dynamics of the Izhikevich neuron model [1] [2] is given by:

\[ \begin{align}\begin{aligned}\frac{d V}{d t} &= 0.04 V^{2}+5 V+140-u+I\\\frac{d u}{d t} &=a(b V-u)\end{aligned}\end{align} \]
\[\begin{split}\text{if} v \geq 30 \text{mV}, \text{then} \begin{cases} v \leftarrow c \\ u \leftarrow u+d \end{cases}\end{split}\]

References

Examples

There is a simple usage example:

import brainpy as bp

neu = bp.dyn.Izhikevich(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 Examples

Model Parameters

Parameter

Init Value

Unit

Explanation

a

0.02

It determines the time scaling of the recovery variable \(u\).

b

0.2

It describes the sensitivity of the recovery variable \(u\) to the sub-threshold fluctuations of the membrane potential \(v\).

c

-65

It describes the after-spike reset value of the membrane potential \(v\) caused by the fast high-threshold \(K^{+}\) conductance.

d

8

It describes after-spike reset of the recovery variable \(u\) caused by slow high-threshold \(Na^{+}\) and \(K^{+}\) conductance.

tau_ref

0

ms

Refractory period length. [ms]

V_th

30

mV

The membrane potential threshold.

Model Variables

Variables name

Initial Value

Explanation

V

-65

Membrane potential.

u

1

Recovery variable.

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 (Optional[Sequence[str]]) – 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.

update(x=None)[source]#

The function to specify the updating rule.

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