Brusselator PDE — Spiral Chemical Waves

The Brusselator is a reaction-diffusion model: ∂u/∂t = Du∇²u + A − (B+1)u + u²v, ∂v/∂t = Dv∇²v + Bu − u²v. Near the Hopf bifurcation B > 1+A², the uniform steady state loses stability and spiral waves spontaneously emerge — rotating chemical wave fronts like those in the Belousov-Zhabotinsky reaction.

A 2.00 B 5.50 Du (×10⁻³) 2.0 Dv (×10⁻³) 8.0 Speed 3

A=2.0, B=5.5 Hopf condition: B > 1+A² = 5.0 → oscillating Turing condition: Dv/Du > (√B+1)² /(B−1−A²) = - Steps: 0