TY - JOUR A1 - Zhang, Xiyun A1 - Pikovskij, Arkadij A1 - Liu, Zonghua T1 - Dynamics of oscillators globally coupled via two mean fields JF - Scientific reports N2 - Many studies of synchronization properties of coupled oscillators, based on the classical Kuramoto approach, focus on ensembles coupled via a mean field. Here we introduce a setup of Kuramoto-type phase oscillators coupled via two mean fields. We derive stability properties of the incoherent state and find traveling wave solutions with different locking patterns; stability properties of these waves are found numerically. Mostly nontrivial states appear when the two fields compete, i.e. one tends to synchronize oscillators while the other one desynchronizes them. Here we identify normal branches which bifurcate from the incoherent state in a usual way, and anomalous branches, appearance of which cannot be described as a bifurcation. Furthermore, hybrid branches combining properties of both are described. In the situations where no stable traveling wave exists, modulated quasiperiodic in time dynamics is observed. Our results indicate that a competition between two coupling channels can lead to a complex system behavior, providing a potential generalized framework for understanding of complex phenomena in natural oscillatory systems. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-02283-1 SN - 2045-2322 VL - 7 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Zaks, Michael A1 - Pikovskij, Arkadij T1 - Chimeras and complex cluster states in arrays of spin-torque oscillators JF - Scientific reports N2 - We consider synchronization properties of arrays of spin-torque nano-oscillators coupled via an RC load. We show that while the fully synchronized state of identical oscillators may be locally stable in some parameter range, this synchrony is not globally attracting. Instead, regimes of different levels of compositional complexity are observed. These include chimera states (a part of the array forms a cluster while other units are desynchronized), clustered chimeras (several clusters plus desynchronized oscillators), cluster state (all oscillators form several clusters), and partial synchronization (no clusters but a nonvanishing mean field). Dynamically, these states are also complex, demonstrating irregular and close to quasiperiodic modulation. Remarkably, when heterogeneity of spin-torque oscillators is taken into account, dynamical complexity even increases: close to the onset of a macroscopic mean field, the dynamics of this field is rather irregular. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-04918-9 SN - 2045-2322 VL - 7 PB - Nature Publ. Group CY - London ER - TY - JOUR A1 - Politi, Antonio A1 - Pikovskij, Arkadij A1 - Ullner, Ekkehard T1 - Chaotic macroscopic phases in one-dimensional oscillators JF - European physical journal special topics N2 - The connection between the macroscopic description of collective chaos and the underlying microscopic dynamics is thoroughly analysed in mean-field models of one-dimensional oscillators. We investigate to what extent infinitesimal perturbations of the microscopic configurations can provide information also on the stability of the corresponding macroscopic phase. In ensembles of identical one-dimensional dynamical units, it is possible to represent the microscopic configurations so as to make transparent their connection with the macroscopic world. As a result, we find evidence of an intermediate, mesoscopic, range of distances, over which the instability is neither controlled by the microscopic equations nor by the macroscopic ones. We examine a whole series of indicators, ranging from the usual microscopic Lyapunov exponents, to the collective ones, including finite-amplitude exponents. A system of pulse-coupled oscillators is also briefly reviewed as an example of non-identical phase oscillators where collective chaos spontaneously emerges. Y1 - 2017 U6 - https://doi.org/10.1140/epjst/e2017-70056-4 SN - 1951-6355 SN - 1951-6401 VL - 226 SP - 1791 EP - 1810 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Goldobin, Denis S. A1 - Pimenova, Anastasiya V. A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij T1 - Competing influence of common noise and desynchronizing coupling on synchronization in the Kuramoto-Sakaguchi ensemble JF - European physical journal special topics N2 - We describe analytically synchronization and desynchronization effects in an ensemble of phase oscillators driven by common noise and by global coupling. Adopting the Ott-Antonsen ansatz, we reduce the dynamics to closed stochastic equations for the order parameters, and study these equations for the cases of populations of identical and nonidentical oscillators. For nonidentical oscillators we demonstrate a counterintuitive effect of divergence of individual frequencies for moderate repulsive coupling, while the order parameter remains large. Y1 - 2017 U6 - https://doi.org/10.1140/epjst/e2017-70039-y SN - 1951-6355 SN - 1951-6401 VL - 226 SP - 1921 EP - 1937 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Pikovskij, Arkadij T1 - Reconstruction of a scalar voltage-based neural field network from observed time series JF - epl : a letters journal exploring the frontiers of physics Y1 - 2017 U6 - https://doi.org/10.1209/0295-5075/119/30004 SN - 0295-5075 SN - 1286-4854 VL - 119 PB - EDP Sciences CY - Mulhouse ER - TY - JOUR A1 - Dolmatova, Anastasiya V. A1 - Goldobin, Denis S. A1 - Pikovskij, Arkadij T1 - Synchronization of coupled active rotators by common noise JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive (synchronizing) or repulsive (desynchronizing). We develop an analytical approach based on a transformation to approximate angle-action variables and averaging over fast rotations. For identical rotators, we describe a transition from full to partial synchrony at a critical value of repulsive coupling. For nonidentical rotators, the most nontrivial effect occurs at moderate repulsive coupling, where a juxtaposition of phase locking with frequency repulsion (anti-entrainment) is observed. We show that the frequency repulsion obeys a nontrivial power law. Y1 - 2017 U6 - https://doi.org/10.1103/PhysRevE.96.062204 SN - 2470-0045 SN - 2470-0053 VL - 96 SP - E10648 EP - E10657 PB - American Physical Society CY - College Park ER - TY - JOUR A1 - Sysoev, Ilya V. A1 - Ponomarenko, Vladimir I. A1 - Pikovskij, Arkadij T1 - Reconstruction of coupling architecture of neural field networks from vector time series JF - Communications in nonlinear science & numerical simulation N2 - 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. KW - Network reconstruction KW - Time series KW - Neurooscillators KW - Time delay Y1 - 2017 U6 - https://doi.org/10.1016/j.cnsns.2017.10.006 SN - 1007-5704 SN - 1878-7274 VL - 57 SP - 342 EP - 351 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Petereit, Johannes A1 - Pikovskij, Arkadij T1 - Chaos synchronization by nonlinear coupling JF - Communications in nonlinear science & numerical simulation N2 - We study synchronization properties of three nonlinearly coupled chaotic maps. Coupling is introduced in such a way, that it cannot be reduced to pairwise terms, but includes combined action of all interacting units. For two models of nonlinear coupling we characterize the transition to complete synchrony, as well as partially synchronized states. Relation to hypernetworks of chaotic units is also discussed. KW - Chaos synchronization KW - Partial synchrony KW - Intermittency KW - Hypernetwork Y1 - 2016 U6 - https://doi.org/10.1016/j.cnsns.2016.09.002 SN - 1007-5704 SN - 1878-7274 VL - 44 SP - 344 EP - 351 PB - Elsevier CY - Amsterdam ER - TY - GEN A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij T1 - Chimeras and complex cluster states in arrays of spin-torque oscillators N2 - We consider synchronization properties of arrays of spin-torque nano-oscillators coupled via an RC load. We show that while the fully synchronized state of identical oscillators may be locally stable in some parameter range, this synchrony is not globally attracting. Instead, regimes of different levels of compositional complexity are observed. These include chimera states (a part of the array forms a cluster while other units are desynchronized), clustered chimeras (several clusters plus desynchronized oscillators), cluster state (all oscillators form several clusters), and partial synchronization (no clusters but a nonvanishing mean field). Dynamically, these states are also complex, demonstrating irregular and close to quasiperiodic modulation. Remarkably, when heterogeneity of spin-torque oscillators is taken into account, dynamical complexity even increases: close to the onset of a macroscopic mean field, the dynamics of this field is rather irregular. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 384 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-402180 ER - TY - JOUR A1 - Zaks, Michael A. A1 - Pikovskij, Arkadij T1 - Chimeras and complex cluster states in arrays of spin-torque oscillators JF - Scientific reports N2 - We consider synchronization properties of arrays of spin-torque nano-oscillators coupled via an RC load. We show that while the fully synchronized state of identical oscillators may be locally stable in some parameter range, this synchrony is not globally attracting. Instead, regimes of different levels of compositional complexity are observed. These include chimera states (a part of the array forms a cluster while other units are desynchronized), clustered chimeras (several clusters plus desynchronized oscillators), cluster state (all oscillators form several clusters), and partial synchronization (no clusters but a nonvanishing mean field). Dynamically, these states are also complex, demonstrating irregular and close to quasiperiodic modulation. Remarkably, when heterogeneity of spin-torque oscillators is taken into account, dynamical complexity even increases: close to the onset of a macroscopic mean field, the dynamics of this field is rather irregular. Y1 - 2017 U6 - https://doi.org/10.1038/s41598-017-04918-9 SN - 2045-2322 VL - 7 PB - Macmillan Publishers Limited CY - London ER - TY - JOUR A1 - Popovych, Oleksandr V. A1 - Lysyansky, Borys A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Tass, Peter A. T1 - Pulsatile desynchronizing delayed feedback for closed-loop deep brain stimulation JF - PLoS one N2 - High-frequency (HF) deep brain stimulation (DBS) is the gold standard for the treatment of medically refractory movement disorders like Parkinson’s disease, essential tremor, and dystonia, with a significant potential for application to other neurological diseases. The standard setup of HF DBS utilizes an open-loop stimulation protocol, where a permanent HF electrical pulse train is administered to the brain target areas irrespectively of the ongoing neuronal dynamics. Recent experimental and clinical studies demonstrate that a closed-loop, adaptive DBS might be superior to the open-loop setup. We here combine the notion of the adaptive high-frequency stimulation approach, that aims at delivering stimulation adapted to the extent of appropriately detected biomarkers, with specifically desynchronizing stimulation protocols. To this end, we extend the delayed feedback stimulation methods, which are intrinsically closed-loop techniques and specifically designed to desynchronize abnormal neuronal synchronization, to pulsatile electrical brain stimulation. We show that permanent pulsatile high-frequency stimulation subjected to an amplitude modulation by linear or nonlinear delayed feedback methods can effectively and robustly desynchronize a STN-GPe network of model neurons and suggest this approach for desynchronizing closed-loop DBS. Y1 - 2017 U6 - https://doi.org/10.1371/journal.pone.0173363 SN - 1932-6203 VL - 12 PB - PLoS CY - San Fransisco ER - TY - JOUR A1 - Smirnov, Lev A. A1 - Osipov, Grigory V. A1 - Pikovskij, Arkadij T1 - Chimera patterns in the Kuramoto-Battogtokh model JF - Journal of physics : A, Mathematical and theoretical N2 - Kuramoto and Battogtokh (2002 Nonlinear Phenom. Complex Syst. 5 380) discovered chimera states represented by stable coexisting synchrony and asynchrony domains in a lattice of coupled oscillators. After a reformulation in terms of a local order parameter, the problem can be reduced to partial differential equations. We find uniformly rotating, spatially periodic chimera patterns as solutions of a reversible ordinary differential equation, and demonstrate a plethora of such states. In the limit of neutral coupling they reduce to analytical solutions in the form of one-and two-point chimera patterns as well as localized chimera solitons. Patterns at weakly attracting coupling are characterized by virtue of a perturbative approach. Stability analysis reveals that only the simplest chimeras with one synchronous region are stable. KW - nonlocal coupled oscillators KW - chimera state KW - coarse-grained order parameter KW - Ott-Antonsen reduction KW - perturbation approach KW - linear stability analysis Y1 - 2017 U6 - https://doi.org/10.1088/1751-8121/aa55f1 SN - 1751-8113 SN - 1751-8121 VL - 50 IS - 8 PB - IOP Publ. Ltd. CY - Bristol ER - TY - JOUR A1 - Bolotov, Maxim I. A1 - Smirnov, Lev A. A1 - Osipov, Grigory V. A1 - Pikovskij, Arkadij T1 - Breathing chimera in a system of phase oscillators JF - JETP Letters N2 - Chimera states consisting of synchronous and asynchronous domains in a medium of nonlinearly coupled phase oscillators have been considered. Stationary inhomogeneous solutions of the Ott-Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. The direct numerical simulation has shown that these structures under certain conditions are transformed to oscillatory (breathing) chimera regimes because of the development of instability. Y1 - 2017 U6 - https://doi.org/10.1134/S0021364017180059 SN - 0021-3640 SN - 1090-6487 VL - 106 SP - 393 EP - 399 PB - Pleiades Publ. CY - New York ER -