Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2008-04-21
Nonlinear Sciences
Chaotic Dynamics
Accepted for publication in CHAOS
Scientific paper
10.1063/1.2911541
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piece-wise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence based indices, namely generalized autocorrelation function $P(t)$, correlation of probability of recurrence (CPR), joint probability of recurrence (JPR) and similarity of probability of recurrence (SPR). We have quantified the different synchronization regimes in terms of these indices. The existence of phase synchronization is also characterized by typical transitions in the Lyapunov exponents of the coupled time-delay systems.
Kurths Juergen
Lakshmanan Meenakshi
Senthilkumar D. V.
No associations
LandOfFree
Transition from phase to generalized synchronization in time-delay systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Transition from phase to generalized synchronization in time-delay systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Transition from phase to generalized synchronization in time-delay systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-36374