PHASE SYNCHRONIZATION OF CHAOTIC OSCILLATORS BY EXTERNAL DRIVING

We extend the notion of phase locking to the case of chaotic oscillato rs. Different definitions of the phase are discussed, and the phase dy namics of a single self-sustained chaotic oscillator subjected to exte rnal force is investigated. We describe regimes where the amplitude of the oscillator remains chaotic and the phase is synchronized by the e xternal force. This effect is demonstrated for periodic and noisy driv ing, This phase synchronization is characterized via direct calculatio n of the phase, as well as by implicit indications, such as the resona nt growth of the discrete component in the power spectrum and the appe arance of a macroscopic average field in an ensemble of driven oscilla tors, The Rossler and the Lorenz systems are shown to provide examples of different phase coherence properties, with different response to t he external force. A relation between the phase synchronization and th e properties of the Lyapunov spectrum is discussed.