# brainpy.dyn.neurons.GIF#

class brainpy.dyn.neurons.GIF(size, V_rest=-70.0, V_reset=-70.0, V_th_inf=-50.0, V_th_reset=-60.0, R=20.0, tau=20.0, a=0.0, b=0.01, k1=0.2, k2=0.02, R1=0.0, R2=1.0, A1=0.0, A2=0.0, V_initializer=OneInit(value=-70.0), I1_initializer=ZeroInit, I2_initializer=ZeroInit, Vth_initializer=OneInit(value=-50.0), noise=None, method='exp_auto', keep_size=False, name=None, mode=NormalMode, spike_fun=<jax._src.custom_derivatives.custom_vjp object>)[source]#

Generalized Integrate-and-Fire model.

Model Descriptions

The generalized integrate-and-fire model 1 is given by

\begin{align}\begin{aligned}&\frac{d I_j}{d t} = - k_j I_j\\&\frac{d V}{d t} = ( - (V - V_{rest}) + R\sum_{j}I_j + RI) / \tau\\&\frac{d V_{th}}{d t} = a(V - V_{rest}) - b(V_{th} - V_{th\infty})\end{aligned}\end{align}

When $$V$$ meet $$V_{th}$$, Generalized IF neuron fires:

\begin{align}\begin{aligned}&I_j \leftarrow R_j I_j + A_j\\&V \leftarrow V_{reset}\\&V_{th} \leftarrow max(V_{th_{reset}}, V_{th})\end{aligned}\end{align}

Note that $$I_j$$ refers to arbitrary number of internal currents.

Model Examples

Model Parameters

 Parameter Init Value Unit Explanation V_rest -70 mV Resting potential. V_reset -70 mV Reset potential after spike. V_th_inf -50 mV Target value of threshold potential $$V_{th}$$ updating. V_th_reset -60 mV Free parameter, should be larger than $$V_{reset}$$. R 20 Membrane resistance. tau 20 ms Membrane time constant. Compute by $$R * C$$. a 0 Coefficient describes the dependence of $$V_{th}$$ on membrane potential. b 0.01 Coefficient describes $$V_{th}$$ update. k1 0.2 Constant pf $$I1$$. k2 0.02 Constant of $$I2$$. R1 0 Free parameter. Describes dependence of $$I_1$$ reset value on $$I_1$$ value before spiking. R2 1 Free parameter. Describes dependence of $$I_2$$ reset value on $$I_2$$ value before spiking. A1 0 Free parameter. A2 0 Free parameter.

Model Variables

 Variables name Initial Value Explanation V -70 Membrane potential. input 0 External and synaptic input current. spike False Flag to mark whether the neuron is spiking. V_th -50 Spiking threshold potential. I1 0 Internal current 1. I2 0 Internal current 2. t_last_spike -1e7 Last spike time stamp.

References

1

Mihalaş, Ştefan, and Ernst Niebur. “A generalized linear integrate-and-fire neural model produces diverse spiking behaviors.” Neural computation 21.3 (2009): 704-718.

2

Teeter, Corinne, Ramakrishnan Iyer, Vilas Menon, Nathan Gouwens, David Feng, Jim Berg, Aaron Szafer et al. “Generalized leaky integrate-and-fire models classify multiple neuron types.” Nature communications 9, no. 1 (2018): 1-15.

__init__(size, V_rest=-70.0, V_reset=-70.0, V_th_inf=-50.0, V_th_reset=-60.0, R=20.0, tau=20.0, a=0.0, b=0.01, k1=0.2, k2=0.02, R1=0.0, R2=1.0, A1=0.0, A2=0.0, V_initializer=OneInit(value=-70.0), I1_initializer=ZeroInit, I2_initializer=ZeroInit, Vth_initializer=OneInit(value=-50.0), noise=None, method='exp_auto', keep_size=False, name=None, mode=NormalMode, spike_fun=<jax._src.custom_derivatives.custom_vjp object>)[source]#

Methods

 __init__(size[, V_rest, V_reset, V_th_inf, ...]) clear_input() Function to clear inputs in the neuron group. dI1(I1, t) dI2(I2, t) dV(V, t, I1, I2, I_ext) dVth(V_th, 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.