Bistability between fixed point and limit cycle — ṙ = μr + r³ − r⁵
r = 0.00 | μ = -0.10
In a subcritical Hopf bifurcation, an unstable limit cycle shrinks onto the stable fixed point at the bifurcation. For μ slightly below zero, the origin and the large stable limit cycle coexist (bistability). A finite perturbation — a "kick" — can escape the basin of attraction and trigger runaway oscillations, with no smooth path back.