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.