brainpy.rates.FeedbackFHN

class brainpy.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, rng=[2415903868  143464255]), y_initializer=Uniform(min_val=0, max_val=0.05, rng=[2415903868  143464255]), method='exp_auto', name=None, mode=None, input_var=True)

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.rates.FeedbackFHN(1, delay=10.)
>>> runner = bp.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, rng=[2415903868  143464255]), y_initializer=Uniform(min_val=0, max_val=0.05, rng=[2415903868  143464255]), method='exp_auto', name=None, mode=None, input_var=True)

Methods

__init__(size[, keep_size, a, b, delay, ...])
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.
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_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([x1, x2])	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	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.