ForcedFitzHughNagumo¶

Systems / ODEs / Chemical & biological systems

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

continuous · ODE3 dimensionsexcitableforced

Interactive: drag to rotate

Definition¶

\[ \begin{aligned} \dot{v} &= curr + f \sin{\left(z \right)} - \frac{v^{3}}{3} + v - w \\ \dot{w} &= \gamma \left(a - b w + v\right) \\ \dot{z} &= \omega \end{aligned} \]

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

State variables: v, w, z

Properties¶

Lyapunov spectrum

TODO — lyapunov_spectrum failed: AttributeError

Kaplan–Yorke dimension

TODO — requires a numeric Lyapunov spectrum

Divergence ∇·f

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

Equilibria

none found (no equilibria)

Use it in TSDynamics¶

import tsdynamics as ts

system = ts.systems.ForcedFitzHughNagumo()
traj = system.run(final_time=100.0, dt=0.01)
ts.plot(traj)

spectrum = ts.analysis.lyapunov_spectrum(system)
ts.analysis.kaplan_yorke_dimension(spectrum)

Reference¶

FitzHugh (1961), Biophys. J. 1, 445-466
doi:10.1016/s0006-3495(61)86902-6

BibTeX

@misc{forcedfitzhughnagumo,
  title = {ForcedFitzHughNagumo system},
  note = {FitzHugh (1961), Biophys. J. 1, 445-466},
  doi = {10.1016/s0006-3495(61)86902-6}
}