TY - JOUR A1 - Vlasov, Vladimir A1 - Komarov, Maxim A1 - Pikovskij, Arkadij T1 - Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling JF - Journal of physics : A, Mathematical and theoretical N2 - We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder-diversity of the intrinsic oscillators' frequencies, and external independent noise forces. Based on the self-consistent formulation, we derive analytic solutions for different synchronous states. We report on various non-trivial transitions from incoherence to synchrony, with the following possible scenarios: simple supercritical transition (similar to classical Kuramoto model); subcritical transition with large area of bistability of incoherent and synchronous solutions; appearance of a symmetric two-cluster solution which can coexist with the regular synchronous state. We show that the interplay between relatively small white noise and finite-size fluctuations can lead to metastability of the asynchronous solution. KW - synchronization KW - bi-harmonic coupling KW - noise Y1 - 2015 U6 - https://doi.org/10.1088/1751-8113/48/10/105101 SN - 1751-8113 SN - 1751-8121 VL - 48 IS - 10 PB - IOP Publ. Ltd. CY - Bristol ER - 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 T1 - Synchronization of a Josephson junction array in terms of global variables JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We consider an array of Josephson junctions with a common LCR load. Application of the Watanabe-Strogatz approach [Physica D 74, 197 (1994)] allows us to formulate the dynamics of the array via the global variables only. For identical junctions this is a finite set of equations, analysis of which reveals the regions of bistability of the synchronous and asynchronous states. For disordered arrays with distributed parameters of the junctions, the problem is formulated as an integro-differential equation for the global variables; here stability of the asynchronous states and the properties of the transition synchrony-asynchrony are established numerically. Y1 - 2013 U6 - https://doi.org/10.1103/PhysRevE.88.022908 SN - 1539-3755 VL - 88 IS - 2 PB - American Physical Society CY - College Park 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 - Vlasov, Vladimir A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij T1 - Dynamics of weakly inhomogeneous oscillator populations: perturbation theory on top of Watanabe-Strogatz integrability JF - Journal of physics : A, Mathematical and theoretical N2 - As has been shown by Watanabe and Strogatz (WS) (1993 Phys. Rev. Lett. 70 2391), a population of identical phase oscillators, sine-coupled to a common field, is a partially integrable system: for any ensemble size its dynamics reduce to equations for three collective variables. Here we develop a perturbation approach for weakly nonidentical ensembles. We calculate corrections to the WS dynamics for two types of perturbations: those due to a distribution of natural frequencies and of forcing terms, and those due to small white noise. We demonstrate that in both cases, the complex mean field for which the dynamical equations are written is close to the Kuramoto order parameter, up to the leading order in the perturbation. This supports the validity of the dynamical reduction suggested by Ott and Antonsen (2008 Chaos 18 037113) for weakly inhomogeneous populations. KW - Kuramoto model KW - oscillator populations KW - integrability KW - perturbation theory Y1 - 2016 U6 - https://doi.org/10.1088/1751-8113/49/31/31LT02 SN - 1751-8113 SN - 1751-8121 VL - 49 PB - IOP Publ. Ltd. CY - Bristol ER -