Phase-synchronized States Research Articles

Periodic phase synchronization in coupled chaotic oscillators.

We investigate the characteristics of temporal phase locking states observed in the route to phase synchronization. It is found that before phase synchronization there is a periodic phase synchronization state characterized by periodic appearance of temporal phase-locking state and that the state leads to local negativeness in one of the vanishing Lyapunov exponents. By taking a statistical measure, we present the evidences of the phenomenon in unidirectionally and mutually coupled chaotic oscillators, respectively. And it is qualitatively discussed that the phenomenon is described by a nonuniform oscillator model in the presence of noise.

Phase synchronization in coupled chaotic oscillators with time delay.

The phase synchronization (PS) of two Rössler oscillators with time-delayed signal coupling is studied. We find that time delay can always lead to PS even when the delay is very long. Moreover, with the increase of time delay, the coupling strength at the transition to PS undergoes a nearly periodic wave distribution. At some fixed time-delayed signal coupling, a PS region is followed by a non-PS region when the coupling strength increases. However, an increase of the coupling leads to the PS state again. This phenomenon occurs in systems with a relatively large PS transition point.

Phase synchronization and its cluster feature in two-dimensional coupled map lattices.

Due to a diffusive nearest-neighbor coupling, phase-synchronized states can emerge in two-dimensional chaotic coupled map lattices. By defining a direction phase (like a spin with up or down direction) as the direction of two sequential iterations of the logistic map, we find several novel kinds of phase synchronization which correspond to four different regions in a phase diagram. For the phase with partial phase synchronization, as the coupling strength epsilon increases to a critical threshold epsilon(c), a percolationlike transition is found in the cluster feature of the direction phases relating to the pattern formation. In addition, a scaling of the percolation probability rho approximately (epsilon-epsilon(c))(beta) with beta=2.1 is obtained. The spatial and time correlation functions of the phase clusters are also discussed.

Phase synchronization of diffusively coupled Rössler oscillators with funnel attractors.

Recently, an antiphase phase-synchronized state in a system of diffusively coupled Rössler oscillators has been reported [Gang Hu et al., Phys. Rev. Lett. 85, 3377 (2000)]. In the current paper this antiphase state is explored in detail. Our interests are concentrated on the comparison with the normal in-phase phase-synchronized state for phase-coherent oscillators and the effect of the lattice size. Our main results are that (i) this antiphase synchronization is only for funnel Rössler attractors and cannot be observed in a system of coupled phase-coherent oscillators; (ii) it can be observed only for intermediate values of the lattice size while it disappears for quite low or large values of the lattice size; and (iii) it is different from the in-phase phase-synchronized state of phase-coherent oscillators in many respects.

Reversible transitions between synchronization states of the cardiorespiratory system.

Phase synchronization between cardiac and respiratory oscillations is investigated during anesthesia in rats. Synchrograms and time evolution of synchronization indices are used to show that the system passes reversibly through a sequence of different phase-synchronized states as the anesthesia level changes, indicating that it can undergo phase transitionlike phenomena. It appears that the synchronization state may be used to characterize the depth of anesthesia.