Pai Chai University, Republic of Korea

Recently synchronization behavior in mutually coupled chaotic oscillators with slight parameter mismatch has been extensively studied because of its potentiality in application to many different disciplines of science and technology. What has been known about it that non-synchronization state transits to lag synchronization through phase jumps and next phase synchronization (PS) as the coupling strength increases. One of the most intriguing subjects among those is PS which is characterized by the coincidence of the phases of two chaotic oscillators within , while their amplitudes remain chaos and uncorrelated each other. A typical behavior here is that one of the vanishing Lyapunov exponents becomes negative. However, before phase synchronization, one can usually observe a negative dip in the Lyapunov exponent. So the aim of our study is to investigate synchronization behavior in this dip and to manifest the full route from non-synchronization state to lag synchronization in coupled chaotic oscillators. When two Rössler oscillators with slight parameter mismatch are coupled with each other, the phase difference of them can be classified into two kinds of dynamics, fast and slow. When the fast dynamics is removed after being averaged over during the time segment of the half period of the slow dynamics, we can observe that the slow dynamic is synchronized periodically at the dip. We call this synchronization phenomenon periodic phase synchronization. In this region, the phase difference of the two oscillators jumps periodically, so that the derivative of it touches the zero line periodically while their phases are synchronized temporally. Before periodic phase synchronization, the two chaotic oscillators are de-synchronized. So what we clarify about the synchronization transition in coupled chaotic oscillators is that non-synchronization state develops to lag synchronization through periodic phase synchronization, next intermittent phase synchronization, and then PS.