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 - 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, 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, 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 - 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 - 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 -