brainpy.dyn.rates.FeedbackFHN#

class brainpy.dyn.rates.FeedbackFHN(size, keep_size=False, a=0.7, b=0.8, delay=10.0, tau=12.5, mu=1.6886, v0=- 1, 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=2107558), y_initializer=Uniform(min_val=0, max_val=0.05, seed=2861067), method='exp_auto', name=None, dt=None, mode=NormalMode)[source]#

FitzHugh-Nagumo model with recurrent neural feedback.

The equation of the feedback FitzHugh-Nagumo model 4 is given by

\[\begin{split}\begin{aligned} \frac{dx}{dt} &= x(t) - \frac{x^3(t)}{3} - y(t) + \mu[x(t-\mathrm{delay}) - x_0] \\ \frac{dy}{dt} &= [x(t) + a - b y(t)] / \tau \end{aligned}\end{split}\]

Model Examples

>>> import brainpy as bp
>>> fhn = bp.dyn.rates.FeedbackFHN(1, delay=10.)
>>> runner = bp.dyn.DSRunner(fhn, inputs=('input', 1.), monitors=['x', 'y'])
>>> runner.run(100.)
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.y, legend='y')
>>> bp.visualize.line_plot(runner.mon.ts, runner.mon.x, legend='x', show=True)

Model Parameters

Parameter

Init Value

Unit

Explanation

a

1

Positive constant

b

1

Positive constant

tau

12.5

ms

Membrane time constant.

delay

10

ms

Synaptic delay time constant.

V_th

1.8

mV

Threshold potential of spike.

v0

-1

mV

Resting potential.

mu

1.8

The feedback strength. When positive, it is a excitatory feedback; when negative, it is a inhibitory feedback.

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

4

Plant, Richard E. (1981). A FitzHugh Differential-Difference Equation Modeling Recurrent Neural Feedback. SIAM Journal on Applied Mathematics, 40(1), 150–162. doi:10.1137/0140012

__init__(size, keep_size=False, a=0.7, b=0.8, delay=10.0, tau=12.5, mu=1.6886, v0=- 1, 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=2107558), y_initializer=Uniform(min_val=0, max_val=0.05, seed=2861067), method='exp_auto', name=None, dt=None, mode=NormalMode)[source]#

Methods

__init__(size[, keep_size, a, b, delay, ...])

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.