FHN#

class brainpy.dyn.FHN(size, keep_size=False, 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, rng=RandomState(Array((), dtype=key<fry>) overlaying: [1006878243 4067659844])), y_initializer=Uniform(min_val=0, max_val=0.05, rng=RandomState(Array((), dtype=key<fry>) overlaying: [1006878243 4067659844])), method='exp_auto', name=None, mode=None, input_var=True)[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.

clear_input()[source]#

Empty function of clearing inputs.

update(inp_x=None, inp_y=None)[source]#

The function to specify the updating rule.