Blowout bifurcation and stability of marginal synchronization of chaos - art. no. 036216

Blowout bifurcations are investigated in a symmetrized extension of the rep lacement method of chaotic synchronization which consists of coupling chaot ic systems via mutually shared variables. The coupled systems are partly li near with respect to variables that are not shared, and that form orthogona l invariant manifolds in the composite system. If the coupled systems are i dentical, marginal (projective) synchronization between them occurs. Breaki ng the symmetry by a small variation of the system parameters leads to a ne w kind of blowout bifurcation in which the transverse stability is exchange d between the orthogonal invariant manifolds. This bifurcation is neither s upercritical nor subcritical. The latter scenarios are also observed as the parameters are further varied, leading to on-off intermittency and the app earance of riddled basins of attraction. Examples using well-known chaotic models are presented.