Brusselator – Chemical Oscillator

Parameters

Rate A (feed)1.00 Rate B (control)3.00 Speed1.0

State

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[X]

—

[Y]

—

Fixed pt X*

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Fixed pt Y*

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Science

The Brusselator (Prigogine, 1968) is a minimal model for autocatalytic chemical oscillations:

dX/dt = A − (B+1)X + X²Y dY/dt = BX − X²Y

Fixed point: X* = A, Y* = B/A. Stability: eigenvalues of Jacobian at fixed point. Hopf bifurcation occurs at B = 1 + A².

B_Hopf = 1 + A²

For B > 1+A², the fixed point destabilizes and a stable limit cycle appears — the system oscillates indefinitely. This models the Belousov–Zhabotinsky reaction.