Brusselator

Chemical oscillator — Hopf bifurcation and Turing patterns

Phase Space

Spatial

Time Series

Parameters

A (feed rate): 1.0 B (cross-cat): 3.0 Du (X diffusion): 0.02 Dv (Y diffusion): 0.5

State

X (mean): —

Y (mean): —

Fixed pt: —

Hopf B*: —

Oscillating: —

Theory

Reactions: A→X, 2X+Y→3X
B+X→Y+D, X→E

ODEs:

Ẋ = A − (B+1)X + X²Y

Ẏ = BX − X²Y

Fixed pt: (A, B/A)
Hopf bifurcation at:

B* = 1 + A²

Oscillates for B > B*