brainmodels.neurons.Izhikevich

class brainmodels.neurons.Izhikevich(size, a=0.02, b=0.2, c=- 65.0, d=8.0, tau_ref=0.0, V_th=30.0, method='euler', **kwargs)[source]

The Izhikevich neuron model.

Model Descriptions

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

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

Model Examples

Model Parameters

Parameter

Init Value

Unit

Explanation

a

0.02

It determines the time scale 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.

References

1

Izhikevich, Eugene M. “Simple model of spiking neurons.” IEEE Transactions on neural networks 14.6 (2003): 1569-1572.

2

Izhikevich, Eugene M. “Which model to use for cortical spiking neurons?.” IEEE transactions on neural networks 15.5 (2004): 1063-1070.

__init__(size, a=0.02, b=0.2, c=- 65.0, d=8.0, tau_ref=0.0, V_th=30.0, method='euler', **kwargs)[source]

Methods

__init__(size[, a, b, c, d, tau_ref, V_th, ...])

build_inputs([inputs, show_code])

build_monitors([show_code])

cpu()

cuda()

derivative(V, u, t, Iext)

ints([method])

Collect all integrators in this node and the children nodes.

load_states(filename[, verbose, check])

Load the model states.

nodes([method, _paths])

Collect all children nodes.

register_constant_delay(key, size, delay[, ...])

Register a constant delay.

run(duration[, dt, report, inputs, extra_func])

The running function.

save_states(filename[, all_vars])

Save the model states.

step(t_and_dt, **kwargs)

to(devices)

tpu()

train_vars([method])

The shortcut for retrieving all trainable variables.

unique_name([name, type])

Get the unique name for this object.

update(_t, _dt)

The function to specify the updating rule.

vars([method])

Collect all variables in this node and the children nodes.

Attributes

implicit_nodes

Used to wrap the implicit children nodes which cannot be accessed by self.xxx

implicit_vars

Used to wrap the implicit variables which cannot be accessed by self.xxx

target_backend

Used to specify the target backend which the model to run.