Limits to chaotic phase synchronization

Phase synchronization in coupled chaotic oscillators, a situation where the phase differences of the oscillators are bounded while their amplitudes remain uncorrelated, has been shown to occur for chaotic attractors having a proper structure of rotation in phase space. As applications of phase synchronization become popular, it is important to understand its limit. Here we show that phase synchronization in the above sense cannot occur for the general class of coupled Lorenz type of chaotic oscillators. For such a system, intermittent synchronization between the dynamical variables sets in as soon as an originally null Lyapunov exponent becomes negative.