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Bubbling and on--off intermittency in bailout embeddings

Cartwright, J.H.E.; Magnasco, M.O.; Piro, O.; Tuval, I.
Physical Review E 68, 016217 (1-7) (2003)

We establish and investigate the conceptual connection between the dynamics of the bailout embedding of a Hamiltonian system and the dynamical regimes associated with the occurrence of bubbling and blowout bifurcations. The roles of the invariant manifold and the dynamics restricted to it --- required in bubbling and blowout bifurcating systems --- are played in the bailout embedding by the embedded Hamiltonian dynamical system. The Hamiltonian nature of the dynamics is precisely the distinctive feature of this instance of a bubbling/blowout bifurcation. The detachment of the embedding trajectories from the original ones can thus be thought of as transient on--off intermittency, and noise-induced avoidance of some regions of the embedded phase space can be recognized as Hamiltonian bubbling.