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Home/Biophysics, Fluids & Geoscience/Coupled FitzHugh–Nagumo Neurons

Coupled FitzHugh–Nagumo Neurons

Two excitable FHN units with diffusive coupling: phase plots, time traces, and synchronization vs coupling strength.

FHN + coupling

0.35
0.52
200

Two identical FitzHugh–Nagumo oscillators with diffusive coupling k on the fast variable: v̇ = v − v³/3 − w + I + k(v_other − v), ẇ = ε(v + a − bw). Raise k to pull trajectories together; phase portrait (v₁,v₂) uses samples after transients.

Measured values

RMS(v₁−v₂) late0.000

Classic FHN reduction of Hodgkin–Huxley; not a quantitative cortical model.

Live graphs

About this model

The FitzHugh–Nagumo system is a two-dimensional reduction of excitable kinetics: a fast activator-like variable v and a slow recovery w produce relaxation oscillations. Diffusive coupling k(v_j − v_i) on the fast variable lets two units synchronize or drift depending on drive I and coupling strength.

Who it's for: Students comparing low-dimensional oscillator models to coupled neurons.

Key terms

  • FitzHugh–Nagumo
  • Coupled oscillators
  • Synchronization
  • Phase space

How it works

Minimal coupled excitable units: synchronization metric and (v₁,v₂) projection illustrate how coupling recruits two slow–fast oscillators.

Frequently asked questions

What does RMS(v₁−v₂) measure?
A simple order parameter for synchrony over the second half of the window: small values mean the trajectories track each other after transients.