FitzHugh-Nagumo Model
A simplified 2D neuron model that captures the essential features of excitability. On a 2D spatial grid, it produces rotating spiral waves — the same patterns seen in cardiac tissue and the Belousov-Zhabotinsky reaction.
dv/dt = v − v³/3 − w + I + D∇²v | dw/dt = ε(v + a − bw)
Richard FitzHugh (1961) and J. Nagumo et al. (1962) independently proposed this two-variable reduction of the Hodgkin-Huxley equations. The variable v represents membrane voltage (fast), while w is a recovery variable (slow).
In 2D space with diffusion, excitable media can sustain rotating spiral waves. These arise from a broken wavefront: one end curls inward and becomes the spiral tip. The tip rotates perpetually because the tissue ahead has recovered from the previous excitation.
Spiral waves in cardiac muscle are associated with dangerous arrhythmias like ventricular fibrillation. Understanding their dynamics is crucial for designing defibrillation protocols.