@article{ToenjesPikovsky2020,
  author    = {T{\"o}njes, Ralf and Pikovsky, Arkady},
  title     = {Low-dimensional description for ensembles of identical phase oscillators subject to Cauchy noise},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {5},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.052315},
  pages     = {5},
  year      = {2020},
  abstract  = {We study ensembles of globally coupled or forced identical phase oscillators subject to independent white Cauchy noise. We demonstrate that if the oscillators are forced in several harmonics, stationary synchronous regimes can be exactly described with a finite number of complex order parameters. The corresponding distribution of phases is a product of wrapped Cauchy distributions. For sinusoidal forcing, the Ott-Antonsen low-dimensional reduction is recovered.},
  language  = {en}
}
@misc{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 = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1291},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-57428},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-574281},
  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{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{Pikovsky2020,
  author    = {Pikovsky, Arkady},
  title     = {Scaling of energy spreading in a disordered Ding-Dong lattice},
  series = {Journal of statistical mechanics: theory and experiment},
  volume    = {2020},
  journal   = {Journal of statistical mechanics: theory and experiment},
  number    = {5},
  publisher = {IOP Publishing Ltd.},
  address   = {Bristol},
  issn      = {1742-5468},
  doi       = {10.1088/1742-5468/ab7e30},
  pages     = {12},
  year      = {2020},
  abstract  = {We study numerical propagation of energy in a one-dimensional Ding-Dong lattice composed of linear oscillators with elastic collisions. Wave propagation is suppressed by breaking translational symmetry, and we consider three ways to do this: position disorder, mass disorder, and a dimer lattice with alternating distances between the units. In all cases the spreading of an initially localized wavepacket is irregular, due to the appearance of chaos, and subdiffusive. For a range of energies and of weak and moderate levels of disorder, we focus on the macroscopic statistical characterization of spreading. Guided by a nonlinear diffusion equation, we establish that the mean waiting times of spreading obey a scaling law in dependence of energy. Moreover, we show that the spreading exponents very weakly depend on the level of disorder.},
  language  = {en}
}
@article{LetellierAbrahamShepelyanskyetal.2021,
  author    = {Letellier, Christophe and Abraham, Ralph and Shepelyansky, Dima L. and Rossler, Otto E. and Holmes, Philip and Lozi, Rene and Glass, Leon and Pikovsky, Arkady and Olsen, Lars F. and Tsuda, Ichiro and Grebogi, Celso and Parlitz, Ulrich and Gilmore, Robert and Pecora, Louis M. and Carroll, Thomas L.},
  title     = {Some elements for a history of the dynamical systems theory},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {31},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {5},
  publisher = {AIP Publishing},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/5.0047851},
  pages     = {20},
  year      = {2021},
  abstract  = {Writing a history of a scientific theory is always difficult because it requires to focus on some key contributors and to "reconstruct" some supposed influences. In the 1970s, a new way of performing science under the name "chaos" emerged, combining the mathematics from the nonlinear dynamical systems theory and numerical simulations. To provide a direct testimony of how contributors can be influenced by other scientists or works, we here collected some writings about the early times of a few contributors to chaos theory. The purpose is to exhibit the diversity in the paths and to bring some elements-which were never published-illustrating the atmosphere of this period. Some peculiarities of chaos theory are also discussed.},
  language  = {en}
}
@article{LepriPikovsky2022,
  author    = {Lepri, Stefano and Pikovsky, Arkady},
  title     = {Phase-locking dynamics of heterogeneous oscillator arrays},
  series = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  volume    = {155},
  journal   = {Chaos, solitons \& fractals : applications in science and engineering ; an interdisciplinary journal of nonlinear science},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0960-0779},
  doi       = {10.1016/j.chaos.2021.111721},
  pages     = {8},
  year      = {2022},
  abstract  = {We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched ran-dom frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically their destruction. Upon change of model parameters, such states are found to become unstable with the generation of localized periodic and chaotic oscillations. For weak nonlinear frequency dispersion, metastability occur akin to the case of almost-conservative systems. We also compare the results with the phase-approximation in which the amplitude dynamics is adiabatically eliminated.},
  language  = {en}
}
@article{GongToenjesPikovsky2020,
  author    = {Gong, Chen Chris and T{\"o}njes, Ralf and Pikovsky, Arkady},
  title     = {Coupled M{\"o}bius maps as a tool to model Kuramoto phase synchronization},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.022206},
  pages     = {12},
  year      = {2020},
  abstract  = {We propose Mobius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.},
  language  = {en}
}
@article{ChigarevKazakovPikovsky2020,
  author    = {Chigarev, Vladimir and Kazakov, Alexey and Pikovsky, Arkady},
  title     = {Kantorovich-Rubinstein-Wasserstein distance between overlapping attractor and repeller},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {30},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {7},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/5.0007230},
  pages     = {10},
  year      = {2020},
  abstract  = {We consider several examples of dynamical systems demonstrating overlapping attractor and repeller. These systems are constructed via introducing controllable dissipation to prototypic models with chaotic dynamics (Anosov cat map, Chirikov standard map, and incompressible three-dimensional flow of the ABC-type on a three-torus) and ergodic non-chaotic behavior (skew-shift map). We employ the Kantorovich-Rubinstein-Wasserstein distance to characterize the difference between the attractor and the repeller, in dependence on the dissipation level.},
  language  = {en}
}
@article{CestnikPikovsky2022,
  author    = {Cestnik, Rok and Pikovsky, Arkady},
  title     = {Hierarchy of exact low-dimensional reductions for populations of coupled oscillators},
  series = {Physical review letters},
  volume    = {128},
  journal   = {Physical review letters},
  number    = {5},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {0031-9007},
  doi       = {10.1103/PhysRevLett.128.054101},
  pages     = {6},
  year      = {2022},
  abstract  = {We consider an ensemble of phase oscillators in the thermodynamic limit, where it is described by a kinetic equation for the phase distribution density. We propose an Ansatz for the circular moments of the distribution (Kuramoto-Daido order parameters) that allows for an exact truncation at an arbitrary number of modes. In the simplest case of one mode, the Ansatz coincides with that of Ott and Antonsen [Chaos 18, 037113 (2008)]. Dynamics on the extended manifolds facilitate higher-dimensional behavior such as chaos, which we demonstrate with a simulation of a Josephson junction array. The findings are generalized for oscillators with a Cauchy-Lorentzian distribution of natural frequencies.},
  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}
}