Non-pairwise Interaction in Oscillatory Ensembles: from Theory to Data Analysis

Pikovsky, Arkady; Rosenblum, Michael G.

doi:10.1007/978-3-030-91374-8_6

Cited by 3 publications

(1 citation statement)

References 33 publications

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“…The importance of phase oscillator models and reduction techniques have been highlighted in various reviews and books 1,6,7 . Recent studies also aim at increasing the range of applicability of phase oscillator models by generalizing the conditions under which reduction techniques are valid [8][9][10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

Synchronization transitions in Kuramoto networks with higher-mode interaction

Berner¹,

Lu²,

Sokolov³

2023

Preprint

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Section: Introductionmentioning

confidence: 99%

Synchronization transitions in Kuramoto networks with higher-mode interaction

Berner¹,

Lu²,

Sokolov³

2023

Preprint

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Introduction to Focus Issue: Dynamics of oscillator populations

Pikovsky

Rosenblum

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Even after about 50 years of intensive research, the dynamics of oscillator populations remain one of the most popular topics in nonlinear science. This Focus Issue brings together studies on such diverse aspects of the problem as low-dimensional description, effects of noise and disorder on synchronization transition, control of synchrony, the emergence of chimera states and chaotic regimes, stability of power grids, etc.

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Inferring connectivity of an oscillatory network via the phase dynamics reconstruction

Rosenblum,

Pikovsky

2023

Front. Netw. Physiol.

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We review an approach for reconstructing oscillatory networks’ undirected and directed connectivity from data. The technique relies on inferring the phase dynamics model. The central assumption is that we observe the outputs of all network nodes. We distinguish between two cases. In the first one, the observed signals represent smooth oscillations, while in the second one, the data are pulse-like and can be viewed as point processes. For the first case, we discuss estimating the true phase from a scalar signal, exploiting the protophase-to-phase transformation. With the phases at hand, pairwise and triplet synchronization indices can characterize the undirected connectivity. Next, we demonstrate how to infer the general form of the coupling functions for two or three oscillators and how to use these functions to quantify the directional links. We proceed with a different treatment of networks with more than three nodes. We discuss the difference between the structural and effective phase connectivity that emerges due to high-order terms in the coupling functions. For the second case of point-process data, we use the instants of spikes to infer the phase dynamics model in the Winfree form directly. This way, we obtain the network’s coupling matrix in the first approximation in the coupling strength.

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Non-pairwise Interaction in Oscillatory Ensembles: from Theory to Data Analysis

Cited by 3 publications

References 33 publications

Synchronization transitions in Kuramoto networks with higher-mode interaction

Synchronization transitions in Kuramoto networks with higher-mode interaction

Introduction to Focus Issue: Dynamics of oscillator populations

Inferring connectivity of an oscillatory network via the phase dynamics reconstruction

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