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Summary: Three Types of Transitions to Phase Synchronization in Coupled Chaotic Oscillators
Grigory V. Osipov,1
Bambi Hu,2,3
Changsong Zhou,4
Mikhail V. Ivanchenko,1
and Ju¨rgen Kurths4
1
Department of Radiophysics, Nizhny Novgorod University, 23, Gagarin Avenue, 603950 Nizhny Novgorod, Russia
2
Center for Nonlinear Studies and Department of Physics, Hong Kong Baptist University, Hong Kong, China
3
Department of Physics, University of Houston, Houston, Texas 77204, USA
4
Institute of Physics, University of Potsdam, 10, Am Neuen Palais, D-14415, Potsdam, Germany
(Received 18 January 2003; published 11 July 2003)
We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic
oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion,
three types of transitions to phase synchronization are found. For phase-coherent attractors this
transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong
phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs
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