@article{TeichmannRosenblum2019,
  author    = {Teichmann, Erik and Rosenblum, Michael},
  title     = {Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {29},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {9},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5118843},
  pages     = {11},
  year      = {2019},
  abstract  = {We numerically and analytically analyze transitions between different synchronous states in a network of globally coupled phase oscillators with attractive and repulsive interactions. The elements within the attractive or repulsive group are identical, but natural frequencies of the groups differ. In addition to a synchronous two-cluster state, the system exhibits a solitary state, when a single oscillator leaves the cluster of repulsive elements, as well as partially synchronous quasiperiodic dynamics. We demonstrate how the transitions between these states occur when the repulsion starts to prevail over attraction.},
  language  = {en}
}
@misc{RosenblumPikovskijKuehnetal.2021,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij and K{\"u}hn, Andrea A. and Busch, Johannes Leon},
  title     = {Real-time estimation of phase and amplitude with application to neural data},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-54963},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-549630},
  pages     = {11},
  year      = {2021},
  abstract  = {Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal's past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient's beta-band brain activity.},
  language  = {en}
}
@article{RosenblumPikovskij2019,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij},
  title     = {Numerical phase reduction beyond the first order approximation},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {29},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {1},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5079617},
  pages     = {6},
  year      = {2019},
  abstract  = {We develop a numerical approach to reconstruct the phase dynamics of driven or coupled self-sustained oscillators. Employing a simple algorithm for computation of the phase of a perturbed system, we construct numerically the equation for the evolution of the phase. Our simulations demonstrate that the description of the dynamics solely by phase variables can be valid for rather strong coupling strengths and large deviations from the limit cycle. Coupling functions depend crucially on the coupling and are generally non-decomposable in phase response and forcing terms. We also discuss the limitations of the approach. Published under license by AIP Publishing.},
  language  = {en}
}
@article{RosenblumPikovskij2018,
  author    = {Rosenblum, Michael and Pikovskij, Arkadij},
  title     = {Efficient determination of synchronization domains from observations of asynchronous dynamics},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {28},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {10},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5037012},
  pages     = {8},
  year      = {2018},
  abstract  = {We develop an approach for a fast experimental inference of synchronization properties of an oscillator. While the standard technique for determination of synchronization domains implies that the oscillator under study is forced with many different frequencies and amplitudes, our approach requires only several observations of a driven system. Reconstructing the phase dynamics from data, we successfully determine synchronization domains of noisy and chaotic oscillators. Our technique is especially important for experiments with living systems where an external action can be harmful and shall be minimized. Published by AIP Publishing.},
  language  = {en}
}