class brainpy.dyn.neurons.AdQuaIF(size, V_rest=- 65.0, V_reset=- 68.0, V_th=- 30.0, V_c=- 50.0, a=1.0, b=0.1, c=0.07, tau=10.0, tau_w=10.0, V_initializer=ZeroInit, w_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, mode=NormalMode, name=None)[source]#

Model Descriptions

\begin{split}\begin{aligned} \tau_m \frac{d V}{d t}&=c(V-V_{rest})(V-V_c) - w + I(t), \\ \tau_w \frac{d w}{d t}&=a(V-V_{rest}) - w, \end{aligned}\end{split}

once the membrane potential reaches the spike threshold,

$\begin{split}V \rightarrow V_{reset}, \\ w \rightarrow w+b.\end{split}$

Model Examples

>>> import brainpy as bp
>>> runner = bp.dyn.DSRunner(group, monitors=['V', 'w'], inputs=('input', 30.))
>>> runner.run(300)
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8)
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.V, ylabel='V')
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.w, ylabel='w', show=True)


Model Parameters

 Parameter Init Value Unit Explanation V_rest -65 mV Resting potential. V_reset -68 mV Reset potential after spike. V_th -30 mV Threshold potential of spike and reset. V_c -50 mV Critical voltage for spike initiation. Must be larger than $$V_{rest}$$. a 1 The sensitivity of the recovery variable $$u$$ to the sub-threshold fluctuations of the membrane potential $$v$$ b .1 The increment of $$w$$ produced by a spike. c .07 Coefficient describes membrane potential update. Larger than 0. tau 10 ms Membrane time constant. tau_w 10 ms Time constant of the adaptation current.

Model Variables

 Variables name Initial Value Explanation V 0 Membrane potential. w 0 Adaptation current. input 0 External and synaptic input current. spike False Flag to mark whether the neuron is spiking. t_last_spike -1e7 Last spike time stamp.

References

1

Izhikevich, E. M. (2004). Which model to use for cortical spiking neurons?. IEEE transactions on neural networks, 15(5), 1063-1070.

2

Touboul, Jonathan. “Bifurcation analysis of a general class of nonlinear integrate-and-fire neurons.” SIAM Journal on Applied Mathematics 68, no. 4 (2008): 1045-1079.

__init__(size, V_rest=- 65.0, V_reset=- 68.0, V_th=- 30.0, V_c=- 50.0, a=1.0, b=0.1, c=0.07, tau=10.0, tau_w=10.0, V_initializer=ZeroInit, w_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, mode=NormalMode, name=None)[source]#

Methods

 __init__(size[, V_rest, V_reset, V_th, V_c, ...]) clear_input() Function to clear inputs in the neuron group. dV(V, t, w, I_ext) dw(w, 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

 derivative 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.