@article{TemirbayevNalibayevZhanabaevetal.2013,
  author    = {Temirbayev, Amirkhan A. and Nalibayev, Yerkebulan D. and Zhanabaev, Zeinulla Zh. and Ponomarenko, Vladimir I. and Rosenblum, Michael},
  title     = {Autonomous and forced dynamics of oscillator ensembles with global nonlinear coupling an experimental study},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {87},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {6},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.87.062917},
  pages     = {11},
  year      = {2013},
  abstract  = {We perform experiments with 72 electronic limit-cycle oscillators, globally coupled via a linear or nonlinear feedback loop. While in the linear case we observe a standard Kuramoto-like synchronization transition, in the nonlinear case, with increase of the coupling strength, we first observe a transition to full synchrony and then a desynchronization transition to a quasiperiodic state. However, in this state the ensemble remains coherent so that the amplitude of the mean field is nonzero, but the frequency of the mean field is larger than frequencies of all oscillators. Next, we analyze effects of common periodic forcing of the linearly or nonlinearly coupled ensemble and demonstrate regimes when the mean field is entrained by the force whereas the oscillators are not.},
  language  = {en}
}
@article{TemirbayevZhanabaevTarasovetal.2012,
  author    = {Temirbayev, Amirkhan A. and Zhanabaev, Zeinulla Zh. and Tarasov, Stanislav B. and Ponomarenko, Vladimir I. and Rosenblum, Michael},
  title     = {Experiments on oscillator ensembles with global nonlinear coupling},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {85},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1539-3755},
  doi       = {10.1103/PhysRevE.85.015204},
  pages     = {4},
  year      = {2012},
  abstract  = {We experimentally analyze collective dynamics of a population of 20 electronic Wien-bridge limit-cycle oscillators with a nonlinear phase-shifting unit in the global feedback loop. With an increase in the coupling strength we first observe formation and then destruction of a synchronous cluster, so that the dependence of the order parameter on the coupling strength is not monotonic. After destruction of the cluster the ensemble remains nevertheless coherent, i.e., it exhibits an oscillatory collective mode (mean field). We show that the system is now in a self-organized quasiperiodic state, predicted in Rosenblum and Pikovsky [Phys. Rev. Lett. 98, 064101 (2007)]. In this state, frequencies of all oscillators are smaller than the frequency of the mean field, so that the oscillators are not locked to the mean field they create and their dynamics is quasiperiodic. Without a nonlinear phase-shifting unit, the system exhibits a standard Kuramoto-like transition to a fully synchronous state. We demonstrate a good correspondence between the experiment and previously developed theory. We also propose a simple measure which characterizes the macroscopic incoherence-coherence transition in a finite-size ensemble.},
  language  = {en}
}
@article{SysoevPonomarenkoPikovskij2017,
  author    = {Sysoev, Ilya V. and Ponomarenko, Vladimir I. and Pikovskij, Arkadij},
  title     = {Reconstruction of coupling architecture of neural field networks from vector time series},
  series = {Communications in nonlinear science \& numerical simulation},
  volume    = {57},
  journal   = {Communications in nonlinear science \& numerical simulation},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {1007-5704},
  doi       = {10.1016/j.cnsns.2017.10.006},
  pages     = {342 -- 351},
  year      = {2017},
  abstract  = {We propose a method of reconstruction of the network coupling matrix for a basic voltage-model of the neural field dynamics. Assuming that the multivariate time series of observations from all nodes are available, we describe a technique to find coupling constants which is unbiased in the limit of long observations. Furthermore, the method is generalized for reconstruction of networks with time-delayed coupling, including the reconstruction of unknown time delays. The approach is compared with other recently proposed techniques.},
  language  = {en}
}