@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}
}
@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}
}