TY - JOUR A1 - Vlasov, Vladimir A1 - Macau, Elbert E. N. A1 - Pikovskij, Arkadij T1 - Synchronization of oscillators in a Kuramoto-type model with generic coupling JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Y1 - 2014 U6 - https://doi.org/10.1063/1.4880835 SN - 1054-1500 SN - 1089-7682 VL - 24 IS - 2 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Vlasov, Vladimir A1 - Pikovskij, Arkadij A1 - Macau, Elbert E. N. T1 - Star-type oscillatory networks with generic Kuramoto-type coupling: A model for "Japanese drums synchrony" JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Y1 - 2015 U6 - https://doi.org/10.1063/1.4938400 SN - 1054-1500 SN - 1089-7682 VL - 25 IS - 12 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Freitas, Celso A1 - Macau, Elbert A1 - Pikovskij, Arkadij T1 - Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We study the Deserter Hubs Model: a Kuramoto-like model of coupled identical phase oscillators on a network, where attractive and repulsive couplings are balanced dynamically due to nonlinearity of interactions. Under weak force, an oscillator tends to follow the phase of its neighbors, but if an oscillator is compelled to follow its peers by a sufficient large number of cohesive neighbors, then it actually starts to act in the opposite manner, i.e., in anti-phase with the majority. Analytic results yield that if the repulsion parameter is small enough in comparison with the degree of the maximum hub, then the full synchronization state is locally stable. Numerical experiments are performed to explore the model beyond this threshold, where the overall cohesion is lost. We report in detail partially synchronous dynamical regimes, like stationary phase-locking, multistability, periodic and chaotic states. Via statistical analysis of different network organizations like tree, scale-free, and random ones, we found a measure allowing one to predict relative abundance of partially synchronous stationary states in comparison to time-dependent ones. (C) 2015 AIP Publishing LLC. Y1 - 2015 U6 - https://doi.org/10.1063/1.4919246 SN - 1054-1500 SN - 1089-7682 VL - 25 IS - 4 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Ramos, Antonio M. T. A1 - Builes-Jaramillo, Alejandro A1 - Poveda, German A1 - Goswami, Bedartha A1 - Macau, Elbert E. N. A1 - Kurths, Jürgen A1 - Marwan, Norbert T1 - Recurrence measure of conditional dependence and applications JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - 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. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevE.95.052206 SN - 2470-0045 SN - 2470-0053 VL - 95 PB - American Physical Society CY - College Park ER -