@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}
}
@phdthesis{Yeldesbay2014,
  author    = {Yeldesbay, Azamat},
  title     = {Complex regimes of synchronization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-73348},
  school      = {Universit{\"a}t Potsdam},
  pages     = {ii, 60},
  year      = {2014},
  abstract  = {Synchronization is a fundamental phenomenon in nature. It can be considered as a general property of self-sustained oscillators to adjust their rhythm in the presence of an interaction. In this work we investigate complex regimes of synchronization phenomena by means of theoretical analysis, numerical modeling, as well as practical analysis of experimental data. As a subject of our investigation we consider chimera state, where due to spontaneous symmetry-breaking of an initially homogeneous oscillators lattice split the system into two parts with different dynamics. Chimera state as a new synchronization phenomenon was first found in non-locally coupled oscillators system, and has attracted a lot of attention in the last decade. However, the recent studies indicate that this state is also possible in globally coupled systems. In the first part of this work, we show under which conditions the chimera-like state appears in a system of globally coupled identical oscillators with intrinsic delayed feedback. The results of the research explain how initially monostable oscillators became effectivly bistable in the presence of the coupling and create a mean field that sustain the coexistence of synchronized and desynchronized states. Also we discuss other examples, where chimera-like state appears due to frequency dependence of the phase shift in the bistable system. In the second part, we make further investigation of this topic by modeling influence of an external periodic force to an oscillator with intrinsic delayed feedback. We made stability analysis of the synchronized state and constructed Arnold tongues. The results explain formation of the chimera-like state and hysteric behavior of the synchronization area. Also, we consider two sets of parameters of the oscillator with symmetric and asymmetric Arnold tongues, that correspond to mono- and bi-stable regimes of the oscillator. In the third part, we demonstrate the results of the work, which was done in collaboration with our colleagues from Psychology Department of University of Potsdam. The project aimed to study the effect of the cardiac rhythm on human perception of time using synchronization analysis. From our part, we made a statistical analysis of the data obtained from the conducted experiment on free time interval reproduction task. We examined how ones heartbeat influences the time perception and searched for possible phase synchronization between heartbeat cycles and time reproduction responses. The findings support the prediction that cardiac cycles can serve as input signals, and is used for reproduction of time intervals in the range of several seconds.},
  language  = {en}
}