Subcritical Andronov-Hopf bifurcation

Fig 11.5.5. A subcritical Andronov-Hopf bifurcation, (a) An attraction basin of a stable focus is bounded by a stable manifold of a saddle periodic orbit, (b) The periodic orbit narrows to the stable focus at /x = 0, and the latter becomes a saddle-focus (1,2). 

Fig 11.5.2. Rigid loss of stability of a stable focus at the origin through a subcritical (Li > 0) Andronov-Hopf bifurcation. 

Summary The set of principal stability boundaries of equilibrium states consists of surfaces of three kinds Si, Sr and Ss. Only the Si-like boundaries are safe. As for periodic orbits, there are nine types of principal stability boundaries among them Se, Sg, Sio, Sn are dangerous, while S2, S3, S4 S5 and Si, S2 2ire safe (the latter two correspond to the subcritical Andronov-Hopf and flip bifurcations, respectively). 

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