Brusselator: Turing Patterns & Oscillations

The Brusselator reaction-diffusion system (∂u/∂t = A − (B+1)u + u²v + D_u∇²u) exhibits Hopf oscillations and Turing instabilities that produce spatial patterns when D_v/D_u is large enough.

Reactions

A (source): 4.5 B (control): 9.0 D_u: 1.0 D_v: 8.0

Turing condition: (D_v/D_u) > [(B−1+A²/B)/(2A)]²
Hopf: B > 1+A². Fixed point: (A, B/A).