Transition to intermittent chaotic synchronization

Coupled chaotic oscillators can exhibit intermittent synchronization in the weakly coupling regime, as characterized by the entrainment of their dynamical variables in random time intervals of finite duration. We find that the transition to intermittent synchronization can be characteristically distinct for geometrically different chaotic attractors. In particular, for coupled phase-coherent chaotic attractors such as those from the Rössler system, the transition occurs immediately as the coupling is increased from zero. For phase-incoherent chaotic attractors such as those in the Lorenz system, the transition occurs only when the coupling is sufficiently strong. A theory based on the behavior of the Lyapunov exponents and unstable periodic orbits is developed to understand these distinct transitions.