brainpy.neurons.Izhikevich

class brainpy.neurons.Izhikevich(*args, input_var=True, spike_fun=None, **kwargs)

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__(*args, input_var=True, spike_fun=None, **kwargs)

Methods

__init__(*args[, input_var, spike_fun])
add_aft_update(key, fun)	Add the after update into this node
add_bef_update(key, fun)	Add the before update into this node
add_inp_fun(key, fun[, label, category])	Add an input function.
clear_input()	Empty function of clearing inputs.
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
dV(V, t, u, I)
du(u, t, V)
get_aft_update(key)	Get the after update of this node by the given key.
get_batch_shape([batch_size])
get_bef_update(key)	Get the before update of this node by the given key.
get_delay_data(identifier, delay_pos, *indices)	Get delay data according to the provided delay steps.
get_delay_var(name)
get_inp_fun(key)	Get the input function.
get_local_delay(var_name, delay_name)	Get the delay at the given identifier (name).
has_aft_update(key)	Whether this node has the after update of the given key.
has_bef_update(key)	Whether this node has the before update of the given key.
init_param(param[, shape, sharding])	Initialize parameters.
init_variable(var_data, batch_or_mode[, ...])	Initialize variables.
inv_scaling(x[, scale])
jit_step_run(i, *args, **kwargs)	The jitted step function for running.
load_state(state_dict, **kwargs)	Load states from a dictionary.
load_state_dict(state_dict[, warn, compatible])	Copy parameters and buffers from state_dict into this module and its descendants.
nodes([method, level, include_self])	Collect all children nodes.
offset_scaling(x[, bias, scale])
register_delay(identifier, delay_step, ...)	Register delay variable.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables[, var_cls])
register_local_delay(var_name, delay_name[, ...])	Register local relay at the given delay time.
reset(*args, **kwargs)	Reset function which reset the whole variables in the model (including its children models).
reset_local_delays([nodes])	Reset local delay variables.
reset_state([batch_size])
return_info()
save_state(**kwargs)	Save states as a dictionary.
setattr(key, value)	rtype: None
state_dict(**kwargs)	Returns a dictionary containing a whole state of the module.
std_scaling(x[, scale])
step_run(i, *args, **kwargs)	The step run function.
sum_current_inputs(*args[, init, label])	Summarize all current inputs by the defined input functions .current_inputs.
sum_delta_inputs(*args[, init, label])	Summarize all delta inputs by the defined input functions .delta_inputs.
sum_inputs(*args, **kwargs)
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
tracing_variable(name, init, shape[, ...])	Initialize the variable which can be traced during computations and transformations.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
tree_flatten()	Flattens the object as a PyTree.
tree_unflatten(aux, dynamic_values)	Unflatten the data to construct an object of this class.
unique_name([name, type_])	Get the unique name for this object.
update([x])	The function to specify the updating rule.
update_local_delays([nodes])	Update local delay variables.
vars([method, level, include_self, ...])	Collect all variables in this node and the children nodes.

Attributes

after_updates
before_updates
cur_inputs
current_inputs
delta_inputs
derivative
implicit_nodes
implicit_vars
mode	Mode of the model, which is useful to control the multiple behaviors of the model.
name	Name of the model.
spk_dtype
supported_modes	Supported computing modes.
varshape	The shape of variables in the neuron group.