Barkley model: spiral waves, tip tracking, and spatiotemporal chaos
Controls
0.75
0.06
0.02
1.0
Step: 0
Pattern: —
Barkley Model:
∂u/∂t = D∇²u + (1/ε)u(1−u)(u−(v+b)/a)
∂v/∂t = u − v
u = excitation (action potential), v = recovery (refractoriness). Spiral waves arise near excitable-oscillatory boundary. At high excitability, spiral tip undergoes Euclidean motion; at critical a, tip meanders (Hopf). Further: spiral breaks up into spatiotemporal chaos — cardiac fibrillation analogue.