Reconstructing phase dynamics of oscillator networks

Kralemann, Björn; Pikovsky, Arkady; Rosenblum, Michael

doi:10.1063/1.3597647

Cited by 85 publications

(91 citation statements)

References 29 publications

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“…To this intent, we calculated the phase trajectories of observed and modeled data, since phases are most sensitive to interaction, and provide description of connectivity within dynamical system which discloses a simple interpretation (Kralemann et al 2011). The first step is to transform given time series y(t) = (y k (t)), k = 1, ..N of each object into a cyclic observable.…”

Section: Modelsmentioning

confidence: 99%

Oscillatory patterns in the light curves of five long-term monitored type 1 active galactic nuclei

Kovačević

Pérez-Hernández

Shapovalova

et al. 2018

Monthly Notices of the Royal Astronomical Society

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A new combined data of 5 well known type 1 AGN are probed with a novel hybrid method in a search for oscillatory behavior. Additional analysis of artificial light curves obtained from the coupled oscillatory models gives confirmation for detected periods that could have physical background. We find periodic variations in the long-term light curves of 3C 390.3, NGC 4151, NGC 5548 and E1821+643, with correlation coefficients larger than 0.6. We show that oscillatory patterns of two binary black hole candidates NGC 5548 and E1821+643 corresponds to qualitatively different dynamical regimes of chaos and stability, respectively. We demonstrate that absence of oscillatory patterns in Arp 102B could be due to a weak coupling between oscillatory mechanisms. This is the first good evidence that 3C 390.3 and Arp 102B, categorized as double-peaked Balmer line objects, have qualitative different dynamics. Our analysis shows a novelty in the oscillatory dynamical patterns of the light curves of these type 1 AGN.

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Section: Modelsmentioning

confidence: 99%

Oscillatory patterns in the light curves of five long-term monitored type 1 active galactic nuclei

Kovačević

Pérez-Hernández

Shapovalova

et al. 2018

Monthly Notices of the Royal Astronomical Society

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“…a small-scale network of oscillators [10,60]. The phase decompositions can be applied for pairwise couplings but, more importantly, joint coupling influences can also be inferred.…”

Section: Discussionmentioning

confidence: 99%

A tutorial on time-evolving dynamical Bayesian inference

Stankovski

Duggento

McClintock

et al. 2014

Eur. Phys. J. Spec. Top.

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Abstract. In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In practice many of the data-generating systems are not only time-variable, but also influenced by neighbouring systems and subject to random fluctuations (noise) from their environments. To encompass problems of this kind, we present a tutorial about the dynamical Bayesian inference of time-evolving coupled systems in the presence of noise. It includes the necessary theoretical description and the algorithms for its implementation. For general programming purposes, a pseudocode description is also given. Examples based on coupled phase and limit-cycle oscillators illustrate the salient features of phase dynamics inference. State domain inference is illustrated with an example of coupled chaotic oscillators. The applicability of the latter example to secure communications based on the modulation of coupling functions is outlined. MatLab codes for implementation of the method, as well as for the explicit examples, accompany the tutorial.

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“…The latter could include the coupling strength either from one system or the other or from both of them. Thus one can detect the strengths of the self-, direct, and common coupling components, or of the phase response curve (PRC) (Kralemann, Pikovsky, and Rosenblum, 2011;Iatsenko et al, 2013;Faes, Porta, and Nollo, 2015). In a similar way, these ideas can be generalized for multivariate coupling in networks of interacting systems.…”

Section: Coupling Strength and Directionalitymentioning

confidence: 99%

Coupling functions: Universal insights into dynamical interaction mechanisms

et al. 2017

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The dynamical systems found in nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how an interaction occurs. A coherent and comprehensive review is presented encompassing the rapid progress made recently in the analysis, understanding, and applications of coupling functions. The basic concepts and characteristics of coupling functions are presented through demonstrative examples of different domains, revealing the mechanisms and emphasizing their multivariate nature. The theory of coupling functions is discussed through gradually increasing complexity from strong and weak interactions to globally coupled systems and networks. A variety of methods that have been developed for the detection and reconstruction of coupling functions from measured data is described. These methods are based on different statistical techniques for dynamical inference. Stemming from physics, such methods are being applied in diverse areas of science and technology, including chemistry, biology, physiology, neuroscience, social sciences, mechanics, and secure communications. This breadth of application illustrates the universality of coupling functions for studying the interaction mechanisms of coupled dynamical systems.

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Reconstructing phase dynamics of oscillator networks

Cited by 85 publications

References 29 publications

Oscillatory patterns in the light curves of five long-term monitored type 1 active galactic nuclei

Oscillatory patterns in the light curves of five long-term monitored type 1 active galactic nuclei

A tutorial on time-evolving dynamical Bayesian inference

Coupling functions: Universal insights into dynamical interaction mechanisms

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