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.