TY  - JOUR
A1  - Senthilkumar, Dharmapuri Vijayan
A1  - Muruganandam, Paulsamy
A1  - Lakshmanan, Muthusamy
T1  - Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators
N2  - Chaos synchronization in a ring of diffusively coupled nonlinear oscillators driven by an external identical oscillator is studied. Based on numerical simulations we show that by introducing additional couplings at (mN(c) + 1)-th oscillators in the ring, where m is an integer and N-c is the maximum number of synchronized oscillators in the ring with a single coupling, the maximum number of oscillators that can be synchronized can be increased considerably beyond the limit restricted by size instability. We also demonstrate that there exists an exponential relation between the number of oscillators that can support stable synchronization in the ring with the external drive and the critical coupling strength epsilon(c) with a scaling exponent gamma. The critical coupling strength is calculated by numerically estimating the synchronization error and is also confirmed from the conditional Lyapunov exponents of the coupled systems. We find that the same scaling relation exists for m couplings between the drive and the ring. Further, we have examined the robustness of the synchronous states against Gaussian white noise and found that the synchronization error exhibits a power-law decay as a function of the noise intensity indicating the existence of both noise-enhanced and noise-induced synchronizations depending on the value of the coupling strength epsilon. In addition, we have found that epsilon(c) shows an exponential decay as a function of the number of additional couplings. These results are demonstrated using the paradigmatic models of Rossler and Lorenz oscillators.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.81.066219
SN  - 1539-3755
ER  - 
TY  - JOUR
A1  - Suresh, R.
A1  - Senthilkumar, Dharmapuri Vijayan
A1  - Lakshmanan, Muthusamy
A1  - Kurths, Jürgen
T1  - Global phase synchronization in an array of time-delay systems
N2  - We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio, and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.
Y1  - 2010
UR  - http://pre.aps.org/
U6  - https://doi.org/10.1103/Physreve.82.016215
SN  - 1539-3755
ER  -