brainpy.dyn.rates.FHN#

class brainpy.dyn.rates.FHN(size, alpha=3.0, beta=4.0, gamma=- 1.5, delta=0.0, epsilon=0.5, tau=20.0, 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=None), y_initializer=Uniform(min_val=0, max_val=0.05, seed=None), method='exp_auto', sde_method=None, keep_size=False, name=None)[source]#

FitzHugh-Nagumo system used in 1.

\[\begin{split}\frac{dx}{dt} = -\alpha V^3 + \beta V^2 + \gamma V - w + I_{ext}\\ \tau \frac{dy}{dt} = (V - \delta - \epsilon w)\end{split}\]
Parameters

  • size (Shape) – The model size.

  • 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

1

Kostova, T., Ravindran, R., & Schonbek, M. (2004). FitzHugh–Nagumo revisited: Types of bifurcations, periodical forcing and stability regions by a Lyapunov functional. International journal of bifurcation and chaos, 14(03), 913-925.

__init__(size, alpha=3.0, beta=4.0, gamma=- 1.5, delta=0.0, epsilon=0.5, tau=20.0, 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=None), y_initializer=Uniform(min_val=0, max_val=0.05, seed=None), method='exp_auto', sde_method=None, keep_size=False, name=None)[source]#

Methods

__init__(size[, alpha, beta, gamma, delta, ...])

dx(x, t, y, x_ext)

dy(y, t, x[, y_ext])

get_delay_data(name, delay_step, *indices)

Get delay data according to the provided delay steps.

ints([method])

Collect all integrators in this node and the children nodes.

load_states(filename[, verbose])

Load the model states.

nodes([method, level, include_self])

Collect all children nodes.

register_delay(name, delay_step, delay_target)

Register delay variable.

register_implicit_nodes(nodes)

register_implicit_vars(variables)

reset()

Reset function which reset the whole variables in the model.

reset_delay(name, delay_target)

Reset the delay variable.

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(t, dt)

The function to specify the updating rule.

update_delay(name, delay_data)

Update the delay according to the delay data.

vars([method, level, include_self])

Collect all variables in this node and the children nodes.

Attributes

global_delay_vars

name

steps