@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{SmirnovBolotovOsipovetal.2021, author = {Smirnov, Lev A. and Bolotov, Maxim I. and Osipov, Grigorij V. and Pikovskij, Arkadij}, title = {Disorder fosters chimera in an array of motile particles}, series = {Physical review : E, Statistical, nonlinear and soft matter physics}, volume = {104}, journal = {Physical review : E, Statistical, nonlinear and soft matter physics}, number = {3}, publisher = {American Physical Society}, address = {Melville, NY}, issn = {2470-0045}, doi = {10.1103/PhysRevE.104.034205}, pages = {8}, year = {2021}, abstract = {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.}, 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{MunyaevSmirnovKostinetal.2020, author = {Munyaev, Vyacheslav O. and Smirnov, Lev A. and Kostin, Vasily A. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Analytical approach to synchronous states of globally coupled noisy rotators}, series = {New journal of physics : the open-access journal for physics}, volume = {22}, journal = {New journal of physics : the open-access journal for physics}, number = {2}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1367-2630}, doi = {10.1088/1367-2630/ab6f93}, pages = {14}, year = {2020}, abstract = {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.}, 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{SmirnovOsipovPikovskij2017, author = {Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Chimera patterns in the Kuramoto-Battogtokh model}, series = {Journal of physics : A, Mathematical and theoretical}, volume = {50}, journal = {Journal of physics : A, Mathematical and theoretical}, number = {8}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {1751-8113}, doi = {10.1088/1751-8121/aa55f1}, pages = {10}, year = {2017}, abstract = {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.}, language = {en} } @misc{BolotovSmirnovOsipovetal.2018, author = {Bolotov, Maxim and Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Complex chimera states in a nonlinearly coupled oscillatory medium}, series = {2018 2nd School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR)}, journal = {2018 2nd School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR)}, publisher = {IEEE}, address = {New York}, isbn = {978-1-5386-5818-5}, doi = {10.1109/DCNAIR.2018.8589210}, pages = {17 -- 20}, year = {2018}, abstract = {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.}, language = {en} } @article{BolotovSmirnovOsipovetal.2017, author = {Bolotov, Maxim I. and Smirnov, Lev A. and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Breathing chimera in a system of phase oscillators}, series = {JETP Letters}, volume = {106}, journal = {JETP Letters}, publisher = {Pleiades Publ.}, address = {New York}, issn = {0021-3640}, doi = {10.1134/S0021364017180059}, pages = {393 -- 399}, year = {2017}, abstract = {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.}, 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{MunyaevSmirnovKostinetal.2020, author = {Munyaev, Vyacheslav and Smirnov, Lev A. and Kostin, Vasily and Osipov, Grigory V. and Pikovskij, Arkadij}, title = {Analytical approach to synchronous states of globally coupled noisy rotators}, series = {New Journal of Physics}, volume = {22}, journal = {New Journal of Physics}, number = {2}, publisher = {Springer Science}, address = {New York}, pages = {15}, year = {2020}, abstract = {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.}, language = {en} }