@article{RamosBuilesJaramilloPovedaetal.2017,
  author    = {Ramos, Antonio M. T. and Builes-Jaramillo, Alejandro and Poveda, German and Goswami, Bedartha and Macau, Elbert E. N. and Kurths, J{\"u}rgen and Marwan, Norbert},
  title     = {Recurrence measure of conditional dependence and applications},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {95},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.95.052206},
  pages     = {8},
  year      = {2017},
  abstract  = {Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Herewe propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.},
  language  = {en}
}
@article{VlasovMacauPikovskij2014,
  author    = {Vlasov, Vladimir and Macau, Elbert E. N. and Pikovskij, Arkadij},
  title     = {Synchronization of oscillators in a Kuramoto-type model with generic coupling},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {24},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {2},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.4880835},
  pages     = {7},
  year      = {2014},
  abstract  = {We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of oscillators to the mean field and to different forces from the mean field on oscillators. We present the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators. As an example, we consider spatially spreaded oscillators for which the coupling properties are determined by finite velocity of signal propagation. (C) 2014 AIP Publishing LLC.},
  language  = {en}
}
@article{VlasovPikovskijMacau2015,
  author    = {Vlasov, Vladimir and Pikovskij, Arkadij and Macau, Elbert E. N.},
  title     = {Star-type oscillatory networks with generic Kuramoto-type coupling: A model for "Japanese drums synchrony"},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {25},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {12},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.4938400},
  pages     = {13},
  year      = {2015},
  abstract  = {We analyze star-type networks of phase oscillators by virtue of two methods. For identical oscillators we adopt the Watanabe-Strogatz approach, which gives full analytical description of states, rotating with constant frequency. For nonidentical oscillators, such states can be obtained by virtue of the self-consistent approach in a parametric form. In this case stability analysis cannot be performed, however with the help of direct numerical simulations we show which solutions are stable and which not. We consider this system as a model for a drum orchestra, where we assume that the drummers follow the signal of the leader without listening to each other and the coupling parameters are determined by a geometrical organization of the orchestra. (C) 2015 AIP Publishing LLC.},
  language  = {en}
}