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We study synchronization transitions in a system of two coupled self-sustained chaotic oscillators. We demonstrate that with the increase of coupling strength the system first undergoes the transition to phase synchronization. With a further increase of coupling, a new synchronous regime is observed, where the states of two oscillators are nearly identical, but one system lags in time to the other. We describe this regime as a state with correlated amplitudes and a constant phase shift. These transitions are traced in the Lyapunov spectrum.
Rosenblum et al. (Mon,) studied this question.