Blowout bifurcation and stability of marginal synchronization of chaos.

Blowout bifurcations are investigated in a symmetrized extension of the replacement method of chaotic synchronization which consists of coupling chaotic systems via mutually shared variables. The coupled systems are partly linear with respect to variables that are not shared, and that form orthogonal invariant manifolds in the composite system. If the coupled systems are identical, marginal (projective) synchronization between them occurs. Breaking the symmetry by a small variation of the system parameters leads to a new kind of blowout bifurcation in which the transverse stability is exchanged between the orthogonal invariant manifolds. This bifurcation is neither supercritical nor subcritical. The latter scenarios are also observed as the parameters are further varied, leading to on-off intermittency and the appearance of riddled basins of attraction. Examples using well-known chaotic models are presented.