@article{SenthilkumarKurths2010,
  author    = {Senthilkumar, Dharmapuri Vijayan and Kurths, J{\"u}rgen},
  title     = {Characteristics and synchronization of time-delay systems driven by a common noise},
  issn      = {1951-6355},
  doi       = {10.1140/epjst/e2010-01273-4},
  year      = {2010},
  abstract  = {We investigate the characteristics of time-delay systems in the presence of Gaussian noise. We show that the delay time embedded in the time series of time-delay system with constant delay cannot be estimated in the presence noise for appropriate values of noise intensity thereby forbidding any possibility of phase space reconstruction. We also demonstrate the existence of complete synchronization between two independent identical time-delay systems driven by a common noise without explicitly establishing any external coupling between them.},
  language  = {en}
}
@article{SureshSenthilkumarLakshmananetal.2010,
  author    = {Suresh, R. and Senthilkumar, Dharmapuri Vijayan and Lakshmanan, Muthusamy and Kurths, J{\"u}rgen},
  title     = {Global phase synchronization in an array of time-delay systems},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.82.016215},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}
@article{SenthilkumarMuruganandamLakshmanan2010,
  author    = {Senthilkumar, Dharmapuri Vijayan and Muruganandam, Paulsamy and Lakshmanan, Muthusamy},
  title     = {Scaling and synchronization in a ring of diffusively coupled nonlinear oscillators},
  issn      = {1539-3755},
  doi       = {10.1103/Physreve.81.066219},
  year      = {2010},
  abstract  = {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.},
  language  = {en}
}