brainpy.dyn.neurons.Izhikevich

class brainpy.dyn.neurons.Izhikevich(size, a=0.02, b=0.2, c=- 65.0, d=8.0, V_th=30.0, tau_ref=0.0, V_initializer=ZeroInit, u_initializer=OneInit(value=1.0), method='exp_auto', keep_size=False, name=None)

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

• Detailed examples to reproduce different firing patterns

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, V_th=30.0, tau_ref=0.0, V_initializer=ZeroInit, u_initializer=OneInit(value=1.0), method='exp_auto', keep_size=False, name=None)

Methods

__init__(size[, a, b, c, d, V_th, tau_ref, ...])
dV(V, t, u, I_ext)
du(u, t, V)
get_delay_data(name, delay_step, *indices)	Get delay data according to the provided delay steps.
ints([method])	Collect all integrators in this node and the children nodes.
load_states(filename[, verbose])	Load the model states.
nodes([method, level, include_self])	Collect all children nodes.
register_delay(name, delay_step, delay_target)	Register delay variable.
register_implicit_nodes(nodes)
register_implicit_vars(variables)
reset()	Reset function which reset the whole variables in the model.
reset_delay(name, delay_target)	Reset the delay variable.
save_states(filename[, variables])	Save the model states.
train_vars([method, level, include_self])	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.
update_delay(name, delay_data)	Update the delay according to the delay data.
vars([method, level, include_self])	Collect all variables in this node and the children nodes.

Attributes

global_delay_vars
name
steps