Brusselator Chemical Oscillator
ẋ=A−(B+1)x+x²y, ẏ=Bx−x²y — Hopf bifurcation at B=1+A²
Phase Portrait (x,y)
Bifurcation Surface B vs A
Parameters
Parameter A:
2.00
Parameter B:
5.50
Trajectories:
5
Speed:
3
Fixed pt (A, B/A):
—
B_Hopf = 1+A²:
—
Current B:
—
Phase:
—
ω_Hopf ≈ A:
—
Brusselator reactions: A→X, B+X→Y+C, 2X+Y→3X, X→D
Fixed point: (A, B/A). Stability: eigenvalues λ = (B−1−A²)/2 ± √Δ
Hopf: B_c = 1+A². Supercritical pitchfork in parameter space.
Time Series x(t) and y(t)