BZ Reaction — Spiral Tip Dynamics

Oregonator model on 2D grid: rigid rotation, meandering, and tip trajectory

Oregonator Parameters

ε (time scale) 0.04

f (stoichiometry) 1.4

q (excitability) 0.002

D_u diffusion 0.5

Display

Show tip trail ON

State

Steps: 0

Regime: —

Belousov-Zhabotinsky Spiral Waves

The BZ reaction is modelled by the Oregonator: ∂u/∂t = [u(1−u) − fv(u−q)/(u+q)] / ε + D_u∇²u, ∂v/∂t = u − v. Here u ≈ [HBrO₂], v ≈ [Ce⁴⁺].

The spiral tip is the point where the excitation front meets the recovery tail. It can undergo rigid rotation (simple orbit) or meandering (epicyclic "petal" patterns) depending on parameters. The transition between these regimes is a Hopf bifurcation of the tip orbit.

The colour map encodes u: blue = resting, red = excited, transitioning through cyan/green. The tip trajectory (white trail) reveals whether rotation is rigid or compound.