class brainpy.neurons.AdExIF(size, V_rest=-65.0, V_reset=-68.0, V_th=-30.0, V_T=-59.9, delta_T=3.48, a=1.0, b=1.0, tau=10.0, tau_w=30.0, tau_ref=None, R=1.0, V_initializer=ZeroInit, w_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, input_var=True, mode=None, name=None)[source]#

Model Descriptions

The adaptive exponential integrate-and-fire model, also called AdEx, is a spiking neuron model with two variables [1] [2].

\begin{split}\begin{aligned} \tau_m\frac{d V}{d t} &= - (V-V_{rest}) + \Delta_T e^{\frac{V-V_T}{\Delta_T}} - Rw + RI(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,

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

The first equation describes the dynamics of the membrane potential and includes an activation term with an exponential voltage dependence. Voltage is coupled to a second equation which describes adaptation. Both variables are reset if an action potential has been triggered. The combination of adaptation and exponential voltage dependence gives rise to the name Adaptive Exponential Integrate-and-Fire model.

The adaptive exponential integrate-and-fire model is capable of describing known neuronal firing patterns, e.g., adapting, bursting, delayed spike initiation, initial bursting, fast spiking, and regular spiking.

Model Examples

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_T -59.9 mV Threshold potential of generating action potential. delta_T 3.48 Spike slope factor. 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. R 1 Membrane resistance. tau 10 ms Membrane time constant. Compute by R * C. tau_w 30 ms Time constant of the adaptation current. tau_ref ms Refractory time.

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. refractory False Flag to mark whether the neuron is in refractory period. t_last_spike -1e7 Last spike time stamp.

References

__init__(size, V_rest=-65.0, V_reset=-68.0, V_th=-30.0, V_T=-59.9, delta_T=3.48, a=1.0, b=1.0, tau=10.0, tau_w=30.0, tau_ref=None, R=1.0, V_initializer=ZeroInit, w_initializer=ZeroInit, noise=None, method='exp_auto', keep_size=False, input_var=True, mode=None, name=None)[source]#

Methods

 __init__(size[, V_rest, V_reset, V_th, V_T, ...]) clear_input() Function to clear inputs in the neuron group. cpu() Move all variable into the CPU device. cuda() Move all variables into the GPU device. 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_state_dict(state_dict[, warn, compatible]) Copy parameters and buffers from state_dict into this module and its descendants. load_states(filename[, verbose]) Load the model states. nodes([method, level, include_self]) Collect all children nodes. register_delay(identifier, delay_step, ...) Register delay variable. register_implicit_nodes(*nodes[, node_cls]) register_implicit_vars(*variables[, var_cls]) reset(*args, **kwargs) 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. state_dict() Returns a dictionary containing a whole state of the module. to(device) Moves all variables into the given device. tpu() Move all variables into the TPU device. 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

 derivative global_delay_data Global delay data, which stores the delay variables and corresponding delay targets. 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.