TY - JOUR A1 - Mau, Erik Thomas Klaus A1 - Rosenblum, Michael T1 - Optimizing charge-balanced pulse stimulation for desynchronization JF - Chaos : an interdisciplinary journal of nonlinear science N2 - Collective synchronization in a large population of self-sustained units appears both in natural and engineered systems. Sometimes this effect is in demand, while in some cases, it is undesirable, which calls for control techniques. In this paper, we focus on pulsatile control, with the goal to either increase or decrease the level of synchrony. We quantify this level by the entropy of the phase distribution. Motivated by possible applications in neuroscience, we consider pulses of a realistic shape. Exploiting the noisy Kuramoto-Winfree model, we search for the optimal pulse profile and the optimal stimulation phase. For this purpose, we derive an expression for the change of the phase distribution entropy due to the stimulus. We relate this change to the properties of individual units characterized by generally different natural frequencies and phase response curves and the population's state. We verify the general result by analyzing a two-frequency population model and demonstrating a good agreement of the theory and numerical simulations. Y1 - 2022 U6 - https://doi.org/10.1063/5.0070036 SN - 1054-1500 SN - 1089-7682 VL - 32 IS - 1 PB - AIP CY - Melville ER - TY - JOUR A1 - Kumar, Mohit A1 - Rosenblum, Michael T1 - Two mechanisms of remote synchronization in a chain of Stuart-Landau oscillators JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - Remote synchronization implies that oscillators interacting not directly but via an additional unit (hub) adjust their frequencies and exhibit frequency locking while the hub remains asynchronous. In this paper, we analyze the mechanisms of remote synchrony in a small network of three coupled Stuart-Landau oscillators using recent results on higher-order phase reduction. We analytically demonstrate the role of two factors promoting remote synchrony. These factors are the nonisochronicity of oscillators and the coupling terms appearing in the secondorder phase approximation. We show a good correspondence between our theory and numerical results for small and moderate coupling strengths. Y1 - 2021 U6 - https://doi.org/10.1103/PhysRevE.104.054202 SN - 2470-0045 SN - 2470-0053 VL - 104 IS - 5 PB - American Physical Society CY - College Park ER - TY - GEN A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Kühn, Andrea A. A1 - Busch, Johannes Leon T1 - Real-time estimation of phase and amplitude with application to neural data T2 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe N2 - 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. T3 - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1241 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-549630 SN - 1866-8372 PB - Universitätsverlag Potsdam CY - Potsdam ER - TY - JOUR A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij A1 - Kühn, Andrea A. A1 - Busch, Johannes Leon T1 - Real-time estimation of phase and amplitude with application to neural data JF - Scientific reports N2 - 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. Y1 - 2021 U6 - https://doi.org/10.1038/s41598-021-97560-5 SN - 2045-2322 VL - 11 PB - Springer Nature CY - London ER - TY - JOUR A1 - Rosenblum, Michael T1 - Controlling collective synchrony in oscillatory ensembles by precisely timed pulses JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We present an efficient technique for control of synchrony in a globally coupled ensemble by pulsatile action. We assume that we can observe the collective oscillation and can stimulate all elements of the ensemble simultaneously. We pay special attention to the minimization of intervention into the system. The key idea is to stimulate only at the most sensitive phase. To find this phase, we implement an adaptive feedback control. Estimating the instantaneous phase of the collective mode on the fly, we achieve efficient suppression using a few pulses per oscillatory cycle. We discuss the possible relevance of the results for neuroscience, namely, for the development of advanced algorithms for deep brain stimulation, a medical technique used to treat Parkinson's disease. Y1 - 2020 U6 - https://doi.org/10.1063/5.0019823 SN - 1054-1500 SN - 1089-7682 VL - 30 IS - 9 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Krylov, Dmitrii A1 - Dylov, Dmitry V. A1 - Rosenblum, Michael T1 - Reinforcement learning for suppression of collective activity in oscillatory ensembles JF - Chaos : an interdisciplinary journal of nonlinear science N2 - We present the use of modern machine learning approaches to suppress self-sustained collective oscillations typically signaled by ensembles of degenerative neurons in the brain. The proposed hybrid model relies on two major components: an environment of oscillators and a policy-based reinforcement learning block. We report a model-agnostic synchrony control based on proximal policy optimization and two artificial neural networks in an Actor-Critic configuration. A class of physically meaningful reward functions enabling the suppression of collective oscillatory mode is proposed. The synchrony suppression is demonstrated for two models of neuronal populations-for the ensembles of globally coupled limit-cycle Bonhoeffer-van der Pol oscillators and for the bursting Hindmarsh-Rose neurons using rectangular and charge-balanced stimuli. Y1 - 2020 U6 - https://doi.org/10.1063/1.5128909 SN - 1054-1500 SN - 1089-7682 VL - 30 IS - 3 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Teichmann, Erik A1 - Rosenblum, Michael T1 - Solitary states and partial synchrony in oscillatory ensembles with attractive and repulsive interactions JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1063/1.5118843 SN - 1054-1500 SN - 1089-7682 VL - 29 IS - 9 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Rosenblum, Michael A1 - Frühwirth, Martha A1 - Moser, Maximilian A1 - Pikovskij, Arkadij T1 - Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia JF - Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences N2 - We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'. KW - phase dynamics KW - point process KW - vagal sympathetic activity KW - autonomic nervous system Y1 - 2019 U6 - https://doi.org/10.1098/rsta.2019.0045 SN - 1364-503X SN - 1471-2962 VL - 377 IS - 2160 PB - Royal Society CY - London ER - TY - JOUR A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij T1 - Nonlinear phase coupling functions: a numerical study JF - Philosophical Transactions of the Royal Society of London, Series A : Mathematical, Physical and Engineering Sciences N2 - Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here, we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the periodically forced Stuart-Landau oscillator as the paradigmatic model, we determine and numerically analyse the coupling functions up to the fourth order in the force strength. We show that the found nonlinear phase coupling functions can be used for predicting synchronization regions of the forced oscillator. KW - phase approximation KW - coupling function KW - phase response curve Y1 - 2019 U6 - https://doi.org/10.1098/rsta.2019.0093 SN - 1364-503X SN - 1471-2962 VL - 377 IS - 2160 PB - Royal Society CY - London ER - TY - JOUR A1 - Rosenblum, Michael A1 - Pikovskij, Arkadij T1 - Numerical phase reduction beyond the first order approximation JF - Chaos : an interdisciplinary journal of nonlinear science N2 - 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. Y1 - 2019 U6 - https://doi.org/10.1063/1.5079617 SN - 1054-1500 SN - 1089-7682 VL - 29 IS - 1 PB - American Institute of Physics CY - Melville ER -