# 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=None, V_initializer=ZeroInit, u_initializer=OneInit(value=1.0), noise=None, method='exp_auto', mode=NormalMode, spike_fun=<jax._src.custom_derivatives.custom_vjp object>, keep_size=False, name=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}
$\begin{split}\text{if} v \geq 30 \text{mV}, \text{then} \begin{cases} v \leftarrow c \\ u \leftarrow u+d \end{cases}\end{split}$

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, V_th=30.0, tau_ref=None, V_initializer=ZeroInit, u_initializer=OneInit(value=1.0), noise=None, method='exp_auto', mode=NormalMode, spike_fun=<jax._src.custom_derivatives.custom_vjp object>, keep_size=False, name=None)[source]#

Methods

 __init__(size[, a, b, c, d, V_th, tau_ref, ...]) clear_input() Function to clear inputs in the neuron group. dV(V, t, u, I_ext) du(u, t, V) get_batch_shape([batch_size]) get_delay_data(identifier, delay_step, *indices) Get delay data according to the provided delay steps. load_states(filename[, verbose]) Load the model states. nodes([method, level, include_self]) Collect all children nodes. offline_fit(target, fit_record) offline_init() online_fit(target, fit_record) online_init() register_delay(identifier, delay_step, ...) Register delay variable. register_implicit_nodes(*nodes, **named_nodes) register_implicit_vars(*variables, ...) reset([batch_size]) Reset function which reset the whole variables in the model. reset_local_delays([nodes]) Reset local delay variables. reset_state([batch_size]) Reset function which reset the states in the model. 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(tdi[, 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

 global_delay_data mode Mode of the model, which is useful to control the multiple behaviors of the model. name Name of the model. varshape The shape of variables in the neuron group.