@article{PimenovaGoldobinRosenblumetal.2016, author = {Pimenova, Anastasiya V. and Goldobin, Denis S. and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Interplay of coupling and common noise at the transition to synchrony in oscillator populations}, series = {Scientific reports}, volume = {6}, journal = {Scientific reports}, publisher = {Nature Publ. Group}, address = {London}, issn = {2045-2322}, doi = {10.1038/srep38518}, pages = {7}, year = {2016}, abstract = {There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.}, 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{TopcuFruehwirthMoseretal.2018, author = {Top{\c{c}}u, {\c{C}}ağda{\c{s}} and Fr{\"u}hwirth, Matthias and Moser, Maximilian and Rosenblum, Michael and Pikovskij, Arkadij}, title = {Disentangling respiratory sinus arrhythmia in heart rate variability records}, series = {Physiological Measurement}, volume = {39}, journal = {Physiological Measurement}, number = {5}, publisher = {IOP Publ. Ltd.}, address = {Bristol}, issn = {0967-3334}, doi = {10.1088/1361-6579/aabea4}, pages = {12}, year = {2018}, abstract = {Objective: Several different measures of heart rate variability, and particularly of respiratory sinus arrhythmia, are widely used in research and clinical applications. For many purposes it is important to know which features of heart rate variability are directly related to respiration and which are caused by other aspects of cardiac dynamics. Approach: Inspired by ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear disentanglement of the heart rate variability into the respiratory-related component and the rest. Main results: The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects. In all cases we show how the disentanglement is manifested in the different measures of heart rate variability. Significance: The suggested technique can be exploited as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate and in cases when effects of other factors on the heart rate variability are in focus.}, language = {en} } @article{PopovychLysyanskyRosenblumetal.2017, author = {Popovych, Oleksandr V. and Lysyansky, Borys and Rosenblum, Michael and Pikovskij, Arkadij and Tass, Peter A.}, title = {Pulsatile desynchronizing delayed feedback for closed-loop deep brain stimulation}, series = {PLoS one}, volume = {12}, journal = {PLoS one}, publisher = {PLoS}, address = {San Fransisco}, issn = {1932-6203}, doi = {10.1371/journal.pone.0173363}, pages = {29}, year = {2017}, abstract = {High-frequency (HF) deep brain stimulation (DBS) is the gold standard for the treatment of medically refractory movement disorders like Parkinson's disease, essential tremor, and dystonia, with a significant potential for application to other neurological diseases. The standard setup of HF DBS utilizes an open-loop stimulation protocol, where a permanent HF electrical pulse train is administered to the brain target areas irrespectively of the ongoing neuronal dynamics. Recent experimental and clinical studies demonstrate that a closed-loop, adaptive DBS might be superior to the open-loop setup. We here combine the notion of the adaptive high-frequency stimulation approach, that aims at delivering stimulation adapted to the extent of appropriately detected biomarkers, with specifically desynchronizing stimulation protocols. To this end, we extend the delayed feedback stimulation methods, which are intrinsically closed-loop techniques and specifically designed to desynchronize abnormal neuronal synchronization, to pulsatile electrical brain stimulation. We show that permanent pulsatile high-frequency stimulation subjected to an amplitude modulation by linear or nonlinear delayed feedback methods can effectively and robustly desynchronize a STN-GPe network of model neurons and suggest this approach for desynchronizing closed-loop DBS.}, language = {en} } @article{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 = {Scientific reports}, volume = {11}, journal = {Scientific reports}, publisher = {Springer Nature}, address = {London}, issn = {2045-2322}, doi = {10.1038/s41598-021-97560-5}, 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{RosenblumPikovskijKurthsetal.2002, author = {Rosenblum, Michael and Pikovskij, Arkadij and Kurths, J{\"u}rgen and Osipov, Grigory V. and Kiss, Istvan Z. and Hudson, J. L.}, title = {Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics}, year = {2002}, language = {en} } @article{PikovskijRosenblumOsipovetal.1997, author = {Pikovskij, Arkadij and Rosenblum, Michael and Osipov, Grigory V. and Kurths, J{\"u}rgen}, title = {Phase synchronization effects in a lattice of nonidentical R{\"o}ssler oscillators}, year = {1997}, language = {en} } @article{RosenblumOsipovPikovskijetal.1997, author = {Rosenblum, Michael and Osipov, Grigory V. and Pikovskij, Arkadij and Kurths, J{\"u}rgen}, title = {Phase synchronization of chaotic oscillators by external driving}, year = {1997}, language = {en} } @article{PikovskijRosenblum2015, author = {Pikovskij, Arkadij and Rosenblum, Michael}, title = {Dynamics of globally coupled oscillators: Progress and perspectives}, series = {Chaos : an interdisciplinary journal of nonlinear science}, volume = {25}, journal = {Chaos : an interdisciplinary journal of nonlinear science}, number = {9}, publisher = {American Institute of Physics}, address = {Melville}, issn = {1054-1500}, doi = {10.1063/1.4922971}, pages = {11}, year = {2015}, abstract = {In this paper, we discuss recent progress in research of ensembles of mean field coupled oscillators. Without an ambition to present a comprehensive review, we outline most interesting from our viewpoint results and surprises, as well as interrelations between different approaches. (c) 2015 AIP Publishing LLC.}, language = {en} } @article{PollatosYeldesbayPikovskijetal.2014, author = {Pollatos, Olga and Yeldesbay, Azamat and Pikovskij, Arkadij and Rosenblum, Michael}, title = {How much time has passed? Ask your heart}, series = {Frontiers in neurorobotics}, volume = {8}, journal = {Frontiers in neurorobotics}, publisher = {Frontiers Research Foundation}, address = {Lausanne}, issn = {1662-5218}, doi = {10.3389/fnbot.2014.00015}, pages = {1 -- 9}, year = {2014}, abstract = {Internal signals like one's heartbeats are centrally processed via specific pathways and both their neural representations as well as their conscious perception (interoception) provide key information for many cognitive processes. Recent empirical findings propose that neural processes in the insular cortex, which are related to bodily signals, might constitute a neurophysiological mechanism for the encoding of duration. Nevertheless, the exact nature of such a proposed relationship remains unclear. We aimed to address this question by searching for the effects of cardiac rhythm on time perception by the use of a duration reproduction paradigm. Time intervals used were of 0.5, 2, 3, 7, 10, 14, 25, and 40s length. In a framework of synchronization hypothesis, measures of phase locking between the cardiac cycle and start/stop signals of the reproduction task were calculated to quantify this relationship. The main result is that marginally significant synchronization indices (Sls) between the heart cycle and the time reproduction responses for the time intervals of 2, 3, 10, 14, and 25s length were obtained, while results were not significant for durations of 0.5, 7, and 40s length. On the single participant level, several subjects exhibited some synchrony between the heart cycle and the time reproduction responses, most pronounced for the time interval of 25s (8 out of 23 participants for 20\% quantile). Better time reproduction accuracy was not related with larger degree of phase locking, but with greater vagal control of the heart. A higher interoceptive sensitivity (IS) was associated with a higher synchronization index (SI) for the 2s time interval only. We conclude that information obtained from the cardiac cycle is relevant for the encoding and reproduction of time in the time span of 2-25s. Sympathovagal tone as well as interoceptive processes mediate the accuracy of time estimation.}, language = {en} }