@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{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{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{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{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} } @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{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} } @misc{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 = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, journal = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe}, number = {2}, issn = {1866-8372}, doi = {10.25932/publishup-52426}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-524261}, pages = {17}, 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{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} } @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} }