@article{BolotovBolotovSmirnovetal.2019, author = {Bolotov, Dmitry and Bolotov, Maxim I. and Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Twisted States in a System of Nonlinearly Coupled Phase Oscillators}, series = {Regular and chaotic dynamics : international scientific journal}, volume = {24}, journal = {Regular and chaotic dynamics : international scientific journal}, number = {6}, publisher = {Pleiades publishing inc}, address = {Moscow}, issn = {1560-3547}, doi = {10.1134/S1560354719060091}, pages = {717 -- 724}, year = {2019}, abstract = {We study the dynamics of the ring of identical phase oscillators with nonlinear nonlocal coupling. Using the Ott - Antonsen approach, the problem is formulated as a system of partial derivative equations for the local complex order parameter. In this framework, we investigate the existence and stability of twisted states. Both fully coherent and partially coherent stable twisted states were found (the latter ones for the first time for identical oscillators). We show that twisted states can be stable starting from a certain critical value of the medium length, or on a length segment. The analytical results are confirmed with direct numerical simulations in finite ensembles.}, language = {en} } @article{BoccalettiKurthsOsipov2002, author = {Boccaletti, Stefano and Kurths, J{\"u}rgen and Osipov, Grigory V.}, title = {The synchronization of chaotic systems}, year = {2002}, language = {en} } @article{OsipovIvanchenkoKurthsetal.2005, author = {Osipov, Grigory V. and Ivanchenko, Mikhail V. and Kurths, J{\"u}rgen and Hu, B.}, title = {Synchronized chaotic intermittent and spiking behavior in coupled map chains}, issn = {1539-3755}, year = {2005}, abstract = {We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks}, language = {en} } @article{BolotovBolotovSmirnovetal.2022, author = {Bolotov, Dmitry and Bolotov, Maxim I. and Smirnov, Lev A. and Osipov, Grigory V. and Pikovsky, Arkady}, title = {Synchronization regimes in an ensemble of phase oscillators coupled through a diffusion field}, series = {Radiophysics and quantum electronics}, volume = {64}, journal = {Radiophysics and quantum electronics}, number = {10}, publisher = {Springer}, address = {New York}, issn = {0033-8443}, doi = {10.1007/s11141-022-10173-4}, pages = {709 -- 725}, year = {2022}, abstract = {We consider an ensemble of identical phase oscillators coupled through a common diffusion field. Using the Ott-Antonsen reduction, we develop dynamical equations for the complex local order parameter and the mean field. The regions of the existence and stability are determined for the totally synchronous, partially synchronous, and asynchronous spatially homogeneous states. A procedure of searching for inhomogeneous states as periodic trajectories of an auxiliary system of the ordinary differential equations is demonstrated. A scenario of emergence of chimera structures from homogeneous synchronous solutions is described.}, language = {en} } @article{IvanchenkoOsipovShalfeevetal.2004, author = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen}, title = {Synchronization of two non-scalar-coupled limit-cycle oscillators}, year = {2004}, abstract = {Being one of the fundamental phenomena in nonlinear science, synchronization of oscillations has permanently remained an object of intensive research. Development of many asymptotic methods and numerical simulations has allowed an understanding and explanation of various phenomena of self-synchronization. But even in the classical case of coupled van der Pol oscillators a full description of all possible dynamical regimes, their mutual transitions and characteristics is still lacking. We present here a study of the phenomenon of mutual synchronization for two non-scalar- coupled non-identical limit-cycle oscillators and analyze phase, frequency and amplitude characteristics of synchronization regimes. A series of bifurcation diagrams that we obtain exhibit various regions of qualitatively different behavior. Among them we find mono-, bi- and multistability regions, beating and "oscillation death" ones; also a region, where one of the oscillators dominates the other one is observed. The frequency characteristics that we obtain reveal three qualitatively different types of synchronization: (i) on the mean frequency (the in-phase synchronization), (ii) with a shift from the mean frequency caused by a conservative coupling term (the anti-phase synchronization), and (iii) on the frequency of one of the oscillators (when one oscillator dominates the other). (C) 2003 Elsevier B.V. All rights reserved}, language = {en} } @article{KurthsRomanoThieletal.2006, author = {Kurths, J{\"u}rgen and Romano, Maria Carmen and Thiel, Marco and Osipov, Grigory V. and Ivanchenko, Mikhail V. and Kiss, Istvan Z. and Hudson, John L.}, title = {Synchronization analysis of coupled noncoherent oscillators}, issn = {0924-090X}, doi = {10.1007/s11071-006-1957-x}, year = {2006}, abstract = {We present two different approaches to detect and quantify phase synchronization in the case of coupled non- phase coherent oscillators. The first one is based on the general idea of curvature of an arbitrary curve. The second one is based on recurrences of the trajectory in phase space. We illustrate both methods in the paradigmatic example of the Rossler system in the funnel regime. We show that the second method is applicable even in the case of noisy data. Furthermore, we extend the second approach to the application of chains of coupled systems, which allows us to detect easily clusters of synchronized oscillators. In order to illustrate the applicability of this approach, we show the results of the algorithm applied to experimental data from a population of 64 electrochemical oscillators}, language = {en} } @article{BolotovSmirnovBubnovaetal.2021, author = {Bolotov, Maxim I. and Smirnov, Lev A. and Bubnova, E. S. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Spatiotemporal regimes in the Kuramoto-Battogtokh system of nonidentical oscillators}, series = {Journal of experimental and theoretical physics}, volume = {132}, journal = {Journal of experimental and theoretical physics}, number = {1}, publisher = {Springer}, address = {Heidelberg [u.a.]}, issn = {1063-7761}, doi = {10.1134/S1063776121010106}, pages = {127 -- 147}, year = {2021}, abstract = {We consider the spatiotemporal states of an ensemble of nonlocally coupled nonidentical phase oscillators, which correspond to different regimes of the long-term evolution of such a system. We have obtained homogeneous, twisted, and nonhomogeneous stationary solutions to the Ott-Antonsen equations corresponding to key variants of the realized collective rotational motion of elements of the medium in question with nonzero mesoscopic characteristics determining the degree of coherence of the dynamics of neighboring particles. We have described the procedures of the search for the class of nonhomogeneous solutions as stationary points of the auxiliary point map and of determining the stability based on analysis of the eigenvalue spectrum of the composite operator. Static and breather cluster regimes have been demonstrated and described, as well as the regimes with an irregular behavior of averaged complex fields including, in particular, the local order parameter.}, language = {en} } @article{SmirnovOsipovPikovskij2018, author = {Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Solitary synchronization waves in distributed oscillator populations}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {98}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {6}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.98.062222}, pages = {062222-1 -- 062222-7}, year = {2018}, abstract = {We demonstrate the existence of solitary waves of synchrony in one-dimensional arrays of oscillator populations with Laplacian coupling. Characterizing each community with its complex order parameter, we obtain lattice equations similar to those of the discrete nonlinear Schrodinger system. Close to full synchrony, we find solitary waves for the order parameter perturbatively, starting from the known phase compactons and kovatons; these solutions are extended numerically to the full domain of possible synchrony levels. For nonidentical oscillators, the existence of dissipative solitons is shown.}, language = {en} } @article{BolotovSmirnovOsipovetal.2018, author = {Bolotov, Maxim I. and Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Simple and complex chimera states in a nonlinearly coupled oscillatory medium}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {28}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {4}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5011678}, pages = {9}, year = {2018}, abstract = {We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. In terms of a local coarse-grained complex order parameter, the problem of finding stationary rotating nonhomogeneous solutions reduces to a third-order ordinary differential equation. This allows finding chimera-type and other inhomogeneous states as periodic orbits of this equation. Stability calculations reveal that only some of these states are stable. We demonstrate that an oscillatory instability leads to a breathing chimera, for which the synchronous domain splits into subdomains with different mean frequencies. Further development of instability leads to turbulent chimeras. Published by AIP Publishing.}, language = {en} } @article{OsipovKurths2002, author = {Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Regular and chaotic phase synchronization of coupled circle maps}, year = {2002}, language = {en} } @article{OsipovPikovskijKurths2002, author = {Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase Synchronization of Chaotic Rotators}, year = {2002}, abstract = {We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.}, language = {en} } @article{RosenblumOsipovPikovskijetal.1997, author = {Rosenblum, Michael and Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillators by external driving}, year = {1997}, language = {en} } @article{ZaksRosenblumPikovskijetal.1997, author = {Zaks, Michael A. and Rosenblum, Michael and Pikovskij, Arkadij and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillations in terms of periodic orbits}, issn = {1054-1500}, year = {1997}, language = {en} } @article{IvanchenkoOsipovShalfeevetal.2004, author = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic intermittent oscillations}, issn = {0031-9007}, year = {2004}, abstract = {We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization}, language = {en} } @article{IvanchenkoOsipovShalfeevetal.2004, author = {Ivanchenko, Mikhail V. and Osipov, Grigory V. and Shalfeev, V. D. and Kurths, J{\"u}rgen}, title = {Phase synchronization in ensembles of bursting oscillators}, issn = {0031-9007}, year = {2004}, abstract = {We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles}, language = {en} } @article{PikovskijRosenblumOsipovetal.1997, author = {Pikovskij, Arkadij and Rosenblum, Michael and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization effects in a lattice of nonidentical R{\"o}ssler oscillators}, year = {1997}, language = {en} } @article{BolotovOsipovPikovskij2016, author = {Bolotov, M. I. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Marginal chimera state at cross-frequency locking of pulse-coupled neural networks}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {93}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, publisher = {American Physical Society}, address = {College Park}, issn = {2470-0045}, doi = {10.1103/PhysRevE.93.032202}, pages = {6}, year = {2016}, abstract = {We consider two coupled populations of leaky integrate-and-fire neurons. Depending on the coupling strength, mean fields generated by these populations can have incommensurate frequencies or become frequency locked. In the observed 2:1 locking state of the mean fields, individual neurons in one population are asynchronous with the mean fields, while in another population they have the same frequency as the mean field. These synchronous neurons form a chimera state, where part of them build a fully synchronized cluster, while other remain scattered. We explain this chimera as a marginal one, caused by a self-organized neutral dynamics of the effective circle map.}, language = {en} } @article{RosenblumPikovskijKurthsetal.2002, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen and Osipov, Grigory V. and Kiss, Istvan Z. and Hudson, J. L.}, title = {Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics}, year = {2002}, language = {en} } @article{SmirnovBolotovBolotovetal.2022, author = {Smirnov, Lev A. and Bolotov, Maxim and Bolotov, Dmitri and Osipov, Grigory V. and Pikovsky, Arkady}, title = {Finite-density-induced motility and turbulence of chimera solitons}, series = {New Journal of Physics}, volume = {24}, journal = {New Journal of Physics}, publisher = {IOP}, address = {London}, issn = {1367-2630}, doi = {10.1088/1367-2630/ac63d9}, pages = {15}, year = {2022}, abstract = {We consider a one-dimensional oscillatory medium with a coupling through a diffusive linear field. In the limit of fast diffusion this setup reduces to the classical Kuramoto-Battogtokh model. We demonstrate that for a finite diffusion stable chimera solitons, namely localized synchronous domain in an infinite asynchronous environment, are possible. The solitons are stable also for finite density of oscillators, but in this case they sway with a nearly constant speed. This finite-density-induced motility disappears in the continuum limit, as the velocity of the solitons is inverse proportional to the density. A long-wave instability of the homogeneous asynchronous state causes soliton turbulence, which appears as a sequence of soliton mergings and creations. As the instability of the asynchronous state becomes stronger, this turbulence develops into a spatio-temporal intermittency.}, language = {en} } @article{GrinesOsipovPikovskij2018, author = {Grines, Evgeny and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Describing dynamics of driven multistable oscillators with phase transfer curves}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {28}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {10}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.5037290}, pages = {6}, year = {2018}, abstract = {Phase response curve is an important tool in the studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multistable oscillators with several stable limit cycles. Under a perturbation, transitions from one oscillating mode to another one may occur. We define phase transfer curves to describe the phase shifts at such transitions. This allows for a construction of one-dimensional maps that characterize periodically kicked multistable oscillators. We show that these maps are good approximations of the full dynamics for large periods of forcing. Published by AIP Publishing.}, language = {en} }