Chemical limit cycle · Hopf bifurcation · phase plane
Parameters
Phase Plane
Time Series
X (species 1): —
Y (species 2): —
Fixed pt: —
Phase: —
ẋ = A − (B+1)x + x²y
ẏ = Bx − x²y
Fixed: (A, B/A)
The Brusselator models autocatalytic chemical reactions. The fixed point (A, B/A) loses stability via a supercritical Hopf bifurcation when B > A² + 1. Below threshold: damped oscillations spiral to fixed point. Above: a stable limit cycle attracts all trajectories. Adjust B to watch the transition from stable focus to self-sustaining oscillation.