Limits to chaotic phase synchronizationL. Zhao1, 2, Y.-C. Lai1, 3, R. Wang4 and J.-Y. Gao4
1 Department of Mathematics, Arizona State University Tempe, AZ 85287, USA
2 Institute of Mathematics and Computer Science, University of Sao Paulo Sao Paulo, Brazil
3 Departments of Electrical Engineering and Physics, Arizona State University Tempe, AZ 85287, USA
4 College of Physics, Jilin University - Changchun 130023, PRC
(Received 12 November 2003; accepted in final form 1 March 2004)
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.
05.45.Xt - Synchronization; coupled oscillators.
05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.
© EDP Sciences 2004