# brainpy.dyn.rates.QIF#

class brainpy.dyn.rates.QIF(size, keep_size=False, tau=1.0, eta=- 5.0, delta=1.0, J=15.0, x_ou_mean=0.0, x_ou_sigma=0.0, x_ou_tau=5.0, y_ou_mean=0.0, y_ou_sigma=0.0, y_ou_tau=5.0, x_initializer=Uniform(min_val=0, max_val=0.05, seed=9592702), y_initializer=Uniform(min_val=0, max_val=0.05, seed=9902554), method='exp_auto', name=None, mode=NormalMode)[source]#

A mean-field model of a quadratic integrate-and-fire neuron population.

Model Descriptions

The QIF population mean-field model, which has been derived from a population of all-to-all coupled QIF neurons in 5. The model equations are given by:

\begin{split}\begin{aligned} \tau \dot{r} &=\frac{\Delta}{\pi \tau}+2 r v \\ \tau \dot{v} &=v^{2}+\bar{\eta}+I(t)+J r \tau-(\pi r \tau)^{2} \end{aligned}\end{split}

where $$r$$ is the average firing rate and $$v$$ is the average membrane potential of the QIF population 5.

This mean-field model is an exact representation of the macroscopic firing rate and membrane potential dynamics of a spiking neural network consisting of QIF neurons with Lorentzian distributed background excitabilities. While the mean-field derivation is mathematically only valid for all-to-all coupled populations of infinite size, it has been shown that there is a close correspondence between the mean-field model and neural populations with sparse coupling and population sizes of a few thousand neurons 6.

Model Parameters

 Parameter Init Value Unit Explanation tau 1 ms the population time constant eta -5. the mean of a Lorenzian distribution over the neural excitability in the population delta 1.0 the half-width at half maximum of the Lorenzian distribution over the neural excitability J 15 the strength of the recurrent coupling inside the population
Parameters
• x_ou_mean (Parameter) – The noise mean of the $$x$$ variable, [mV/ms]

• y_ou_mean (Parameter) – The noise mean of the $$y$$ variable, [mV/ms].

• x_ou_sigma (Parameter) – The noise intensity of the $$x$$ variable, [mV/ms/sqrt(ms)].

• y_ou_sigma (Parameter) – The noise intensity of the $$y$$ variable, [mV/ms/sqrt(ms)].

• x_ou_tau (Parameter) – The timescale of the Ornstein-Uhlenbeck noise process of $$x$$ variable, [ms].

• y_ou_tau (Parameter) – The timescale of the Ornstein-Uhlenbeck noise process of $$y$$ variable, [ms].

References

5(1,2)

E. Montbrió, D. Pazó, A. Roxin (2015) Macroscopic description for networks of spiking neurons. Physical Review X, 5:021028, https://doi.org/10.1103/PhysRevX.5.021028.

6

R. Gast, H. Schmidt, T.R. Knösche (2020) A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation. Neural Computation 32.9 (2020): 1615-1634.

__init__(size, keep_size=False, tau=1.0, eta=- 5.0, delta=1.0, J=15.0, x_ou_mean=0.0, x_ou_sigma=0.0, x_ou_tau=5.0, y_ou_mean=0.0, y_ou_sigma=0.0, y_ou_tau=5.0, x_initializer=Uniform(min_val=0, max_val=0.05, seed=9592702), y_initializer=Uniform(min_val=0, max_val=0.05, seed=9902554), method='exp_auto', name=None, mode=NormalMode)[source]#

Methods

 __init__(size[, keep_size, tau, eta, delta, ...]) clear_input() Function to clear inputs in the neuron group. dx(x, t, y, x_ext) dy(y, t, x, y_ext) 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.