Hopf Bifurcation Explorer

Watch a stable fixed point become a limit cycle as μ crosses zero

System:
ẋ = μx − ωy − x(x²+y²)
ẏ = ωx + μy − y(x²+y²)

Regime: stable focus

μ < 0 → spiral sink
μ = 0 → bifurcation
μ > 0 → limit cycle
r* = √μ