@article{RosenblumPikovskij2015, author = {Rosenblum, Michael and Pikovskij, Arkadij}, title = {Two types of quasiperiodic partial synchrony in oscillator ensembles}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, 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.92.012919}, pages = {8}, year = {2015}, abstract = {We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different quasiperiodic states. We present an example of a bifurcation diagram, where we show the borderlines for all these transitions, as well as domain of bistability.}, language = {en} } @misc{KomarovPikovskij2015, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {The Kuramoto model of coupled oscillators with a bi-harmonic coupling function (vol 289, pg 18, 2014)}, series = {Physica :D, Nonlinear phenomena}, volume = {313}, journal = {Physica :D, Nonlinear phenomena}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0167-2789}, doi = {10.1016/j.physd.2015.11.001}, pages = {117 -- 117}, year = {2015}, language = {en} } @article{VlasovKomarovPikovskij2015, author = {Vlasov, Vladimir and Komarov, Maxim and Pikovskij, Arkadij}, title = {Synchronization transitions in ensembles of noisy oscillators with bi-harmonic coupling}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {48}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {10}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8113/48/10/105101}, pages = {16}, year = {2015}, abstract = {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.}, 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} } @article{FreitasMacauPikovskij2015, author = {Freitas, Celso and Macau, Elbert and Pikovskij, Arkadij}, title = {Partial synchronization in networks of non-linearly coupled oscillators: The Deserter Hubs Model}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {25}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {4}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4919246}, pages = {8}, year = {2015}, abstract = {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.}, language = {en} } @article{Pikovskij2015, author = {Pikovskij, Arkadij}, title = {Maximizing Coherence of Oscillations by External Locking}, series = {Physical review letters}, volume = {115}, journal = {Physical review letters}, number = {7}, publisher = {American Physical Society}, address = {College Park}, issn = {0031-9007}, doi = {10.1103/PhysRevLett.115.070602}, pages = {5}, year = {2015}, abstract = {We study how coherence of noisy oscillations can be optimally enhanced by external locking. Based on the condition of minimizing the phase diffusion constant, we find the optimal forcing explicitly in the limits of small and large noise, in dependence of the phase sensitivity of the oscillator. We show analytically that the form of the optimal force bifurcates with the noise intensity; this is confirmed by the analysis of an optimal locking forcing for an experimentally obtained phase sensitivity of a neural cell. In the limit of small noise, the results are compared with purely deterministic conditions of optimal locking.}, language = {en} } @article{KomarovPikovskij2015, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {Intercommunity resonances in multifrequency ensembles of coupled oscillators}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, 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.92.012906}, pages = {11}, year = {2015}, abstract = {We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to the resonance 2 : 1 is considered in detail. We construct uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross coupling across the frequencies can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross coupling is accompanied by a huge multiplicity of distinct synchronous solutions, which is directly related to a multibranch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy phase locking and lead to chaos of mean fields.}, language = {en} } @article{Pikovskij2015, author = {Pikovskij, Arkadij}, title = {First and second sound in disordered strongly nonlinear lattices: numerical study}, series = {Journal of statistical mechanics: theory and experiment}, journal = {Journal of statistical mechanics: theory and experiment}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1742-5468}, doi = {10.1088/1742-5468/2015/08/P08007}, pages = {10}, year = {2015}, abstract = {We study numerically secondary modes on top of a chaotic state in disordered nonlinear lattices. Two basic models are considered, with or without a local on-site potential. By performing periodic spatial modulation of displacement and kinetic energy, and following the temporal evolution of the corresponding spatial profiles, we reveal different modes which can be interpreted as first and second sound.}, language = {en} } @article{KomarovPikovskij2015, author = {Komarov, Maxim and Pikovskij, Arkadij}, title = {Finite-size-induced transitions to synchrony in oscillator ensembles with nonlinear global coupling}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {92}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {2}, publisher = {American Physical Society}, address = {College Park}, issn = {1539-3755}, doi = {10.1103/PhysRevE.92.020901}, pages = {5}, year = {2015}, abstract = {We report on finite-sized-induced transitions to synchrony in a population of phase oscillators coupled via a nonlinear mean field, which microscopically is equivalent to a hypernetwork organization of interactions. Using a self-consistent approach and direct numerical simulations, we argue that a transition to synchrony occurs only for finite-size ensembles and disappears in the thermodynamic limit. For all considered setups, which include purely deterministic oscillators with or without heterogeneity in natural oscillatory frequencies, and an ensemble of noise-driven identical oscillators, we establish scaling relations describing the order parameter as a function of the coupling constant and the system size.}, language = {en} } @article{PikovskijRosenblum2015, author = {Pikovskij, Arkadij and Rosenblum, Michael}, title = {Dynamics of globally coupled oscillators: Progress and perspectives}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {25}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {9}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4922971}, pages = {11}, year = {2015}, abstract = {In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches. (c) 2015 AIP Publishing LLC.}, language = {en} }