From Phase to Lag Synchronization in Coupled Chaotic Oscillators

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.