TY  - JOUR
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Solitary synchronization waves in distributed oscillator populations
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - 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.
Y1  - 2018
U6  - https://doi.org/10.1103/PhysRevE.98.062222
SN  - 2470-0045
SN  - 2470-0053
VL  - 98
IS  - 6
SP  - 062222-1
EP  - 062222-7
PB  - American Physical Society
CY  - College Park
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  - Smirnov, Lev A.
A1  - Bolotov, Maxim I.
A1  - Osipov, Grigorij V.
A1  - Pikovskij, Arkadij
T1  - Disorder fosters chimera in an array of motile particles
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We consider an array of nonlocally coupled oscillators on a ring, which for equally spaced units possesses a Kuramoto-Battogtokh chimera regime and a synchronous state. We demonstrate that disorder in oscillators positions leads to a transition from the synchronous to the chimera state. For a static (quenched) disorder we find that the probability of synchrony survival depends on the number of particles, from nearly zero at small populations to one in the thermodynamic limit. Furthermore, we demonstrate how the synchrony gets destroyed for randomly (ballistically or diffusively) moving oscillators. We show that, depending on the number of oscillators, there are different scalings of the transition time with this number and the velocity of the units.
Y1  - 2021
U6  - https://doi.org/10.1103/PhysRevE.104.034205
SN  - 2470-0045
SN  - 2470-0053
VL  - 104
IS  - 3
PB  - American Physical Society
CY  - Melville, NY
ER  - 
TY  - JOUR
A1  - Smirnov, Lev A.
A1  - Bolotov, Maxim
A1  - Bolotov, Dmitri
A1  - Osipov, Grigory V.
A1  - Pikovsky, Arkady
T1  - Finite-density-induced motility and turbulence of chimera solitons
JF  - New Journal of Physics
N2  - 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.
KW  - chimera
KW  - soliton
KW  - finite-size effects
Y1  - 2022
U6  - https://doi.org/10.1088/1367-2630/ac63d9
SN  - 1367-2630
VL  - 24
PB  - IOP
CY  - London
ER  - 
TY  - JOUR
A1  - Munyaev, Vyacheslav
A1  - Smirnov, Lev A.
A1  - Kostin, Vasily
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Analytical approach to synchronous states of globally coupled noisy rotators
JF  - New Journal of Physics
N2  - We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
KW  - coupled rotators
KW  - synchronization transition
KW  - hysteresis
KW  - Kuramoto model
KW  - noisy systems
Y1  - 2019
VL  - 22
IS  - 2
PB  - Springer Science
CY  - New York
ER  - 
TY  - GEN
A1  - Munyaev, Vyacheslav
A1  - Smirnov, Lev A.
A1  - Kostin, Vasily
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Analytical approach to synchronous states of globally coupled noisy rotators
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1188 
KW  - coupled rotators
KW  - synchronization transition
KW  - hysteresis
KW  - Kuramoto model
KW  - noisy systems
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-524261
SN  - 1866-8372
IS  - 2
ER  - 
TY  - JOUR
A1  - Munyaev, Vyacheslav O.
A1  - Smirnov, Lev A.
A1  - Kostin, Vasily A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Analytical approach to synchronous states of globally coupled noisy rotators
JF  - New journal of physics : the open-access journal for physics
N2  - We study populations of globally coupled noisy rotators (oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the model is reduced to the Kuramoto model of coupled noise oscillators. These approaches provide also analytical criteria distinguishing supercritical and subcritical transitions to the desynchronized state and indicate the universality of such transitions in rotator ensembles. All the obtained analytical results are confirmed by the numerical ones, both by direct simulations of the large ensembles and by solution of the associated Fokker-Planck equation. We also propose generalizations of the developed approaches for setups where different rotators parameters (natural frequencies, masses, noise intensities, strengths and phase shifts in coupling) are dispersed.
KW  - coupled rotators
KW  - synchronization transition
KW  - hysteresis
KW  - Kuramoto
KW  - model
KW  - noisy systems
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/ab6f93
SN  - 1367-2630
VL  - 22
IS  - 2
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - GEN
A1  - Bolotov, Maxim
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Complex chimera states in a nonlinearly coupled oscillatory medium
T2  - 2018 2nd School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR)
N2  - We consider chimera states in a one-dimensional medium of nonlinear nonlocally coupled phase oscillators. Stationary inhomogeneous solutions of the Ott-Antonsen equation for a complex order parameter that correspond to fundamental chimeras have been constructed. Stability calculations reveal that only some of these states are stable. The direct numerical simulation has shown that these structures under certain conditions are transformed to breathing chimera regimes because of the development of instability. Further development of instability leads to turbulent chimeras.
KW  - phase oscillator
KW  - nonlocal coupling
KW  - synchronization
KW  - chimera state
KW  - partial synchronization
KW  - phase lag
KW  - nonlinear dynamics
Y1  - 2018
SN  - 978-1-5386-5818-5
U6  - https://doi.org/10.1109/DCNAIR.2018.8589210
SP  - 17
EP  - 20
PB  - IEEE
CY  - New York
ER  - 
TY  - JOUR
A1  - Bolotov, Maxim I.
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Simple and complex chimera states in a nonlinearly coupled oscillatory medium
JF  - Chaos : an interdisciplinary journal of nonlinear science
N2  - 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.
Y1  - 2018
U6  - https://doi.org/10.1063/1.5011678
SN  - 1054-1500
SN  - 1089-7682
VL  - 28
IS  - 4
PB  - American Institute of Physics
CY  - Melville
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  - 
TY  - JOUR
A1  - Bolotov, Maxim I.
A1  - Smirnov, Lev A.
A1  - Bubnova, E. S.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Spatiotemporal regimes in the Kuramoto-Battogtokh system of nonidentical oscillators
JF  - Journal of experimental and theoretical physics
N2  - 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.
Y1  - 2021
U6  - https://doi.org/10.1134/S1063776121010106
SN  - 1063-7761
SN  - 1090-6509
VL  - 132
IS  - 1
SP  - 127
EP  - 147
PB  - Springer
CY  - Heidelberg [u.a.]
ER  - 
TY  - JOUR
A1  - Bolotov, Dmitry
A1  - Bolotov, Maxim I.
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovsky, Arkady
T1  - Synchronization regimes in an ensemble of phase oscillators coupled through a diffusion field
JF  - Radiophysics and quantum electronics
N2  - 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.
Y1  - 2022
U6  - https://doi.org/10.1007/s11141-022-10173-4
SN  - 0033-8443
SN  - 1573-9120
VL  - 64
IS  - 10
SP  - 709
EP  - 725
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Bolotov, Dmitry
A1  - Bolotov, Maxim I.
A1  - Smirnov, Lev A.
A1  - Osipov, Grigory V.
A1  - Pikovskij, Arkadij
T1  - Twisted States in a System of Nonlinearly Coupled Phase Oscillators
JF  - Regular and chaotic dynamics : international scientific journal
N2  - 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.
KW  - twisted state
KW  - phase oscillators
KW  - nonlocal coupling
KW  - Ott - Antonsen reduction
KW  - stability analysis
Y1  - 2019
U6  - https://doi.org/10.1134/S1560354719060091
SN  - 1560-3547
SN  - 1468-4845
VL  - 24
IS  - 6
SP  - 717
EP  - 724
PB  - Pleiades publishing inc
CY  - Moscow
ER  -