ForcedFitzHughNagumo

Systems / ODEs / Chemical & biological systems

The forced FitzHugh–Nagumo excitable cell — periodic stimulation of a spiking neuron.

continuous · ODE3 dimensionsexcitableforced

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Definition

\[ \begin{aligned} \dot{y_{0}} &= curr + f \sin{\left(y_{2} \right)} - \frac{y_{0}^{3}}{3} + y_{0} - y_{1} \\ \dot{y_{1}} &= \gamma \left(a - b y_{1} + y_{0}\right) \\ \dot{y_{2}} &= \omega \end{aligned} \]

Parameters

Symbol	Default	Role
a	0.7	constant of the slow recovery dynamics
b	0.8	constant of the slow recovery dynamics
curr	0.965	constant baseline stimulus current
f	0.400823	amplitude of the periodic stimulus
gamma	0.08	recovery (slow-variable) timescale factor
omega	0.0436508	angular frequency of the periodic stimulus

Properties

Lyapunov spectrum

$+0.0005715,\; -0.8265,\; 0$
computed at build

Kaplan–Yorke dimension

$D_{KY} = 2.001$

Divergence ∇·f

$\nabla\!\cdot f = - b \gamma - y_{0}^{2} + 1$
state-dependent

Equilibria

none found (no equilibria)

Define it in TSDynamics

import tsdynamics as ts

sys = ts.systems.ForcedFitzHughNagumo()
traj = sys.integrate(final_time=100.0, dt=0.01)

exps = sys.lyapunov_spectrum()
ts.kaplan_yorke_dimension(exps)

Reference

FitzHugh (1961), Biophys. J. 1, 445-466

BibTeX

@misc{forcedfitzhughnagumo,
  title = {ForcedFitzHughNagumo system},
  note = {FitzHugh (1961), Biophys. J. 1, 445-466}
}