Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators

Blaha, Karen; Pikovsky, Arkady; Rosenblum, Michael G.; Clark, Matthew; Rusin, Craig G.; Hudson, John L.

doi:10.1103/physreve.84.046201

Cited by 26 publications

(32 citation statements)

References 31 publications

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“…From Galán, Ermentrout, and Urban, 2005. Kinoshita, 2006;Kiss et al, 2007;Tokuda et al, 2007;Blaha et al, 2011;Tokuda, Wickramasinghe, and Kiss, 2013;Kori et al, 2014). Experiments on chemical, or electrochemical, oscillations provide a convenient way of studying and manipulating interactions and coupling functions under controlled laboratory conditions.…”

Section: A Chemistrymentioning

confidence: 99%

“…IV.B.3. Also, to capture the whole nature of the interaction of electrochemical oscillations (and not only the synchronization-related ones) the coupling functions were reconstructed in the full two-dimensional (ϕ 1 ; ϕ 2 ) space, i.e., not only for the one-dimensional diffusive coupling difference Δϕ ¼ ϕ 2 − ϕ 1 (Blaha et al, 2011).…”

Section: A Chemistrymentioning

confidence: 99%

“…1) and to good effect: in chemistry, for understanding, effecting, or predicting interactions between oscillatory electrochemical reactions (Miyazaki and Kinoshita, 2006;Kiss et al, 2007;Tokuda et al, 2007;Blaha et al, 2011;Kori et al, 2014); in cardiorespiratory physiology Iatsenko et al, 2013;Ticcinelli et al, 2017) for reconstruction of the human cardiorespiratory coupling function and phase resetting curve, for assessing cardiorespiratory time variability, and for studying the evolution of the cardiorespiratory coupling functions with age; in neuroscience for revealing the cross-frequency coupling functions between neural oscillations (Stankovski et al, 2015); and polyrithmic behavior in neuronal circuits (Wojcik et al, 2014;Schwabedal, Knapper, and Shilnikov, 2016); in social sciences for determining the function underlying the interactions between democracy and economic growth ; for mechanical interactions between coupled metronomes (Kralemann et al, 2008); and in secure communications where a new protocol was developed explicitly based on amplitude coupling functions (Stankovski, McClintock, and Stefanovska, 2014).…”

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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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Section: A Chemistrymentioning

confidence: 99%

Section: A Chemistrymentioning

confidence: 99%

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confidence: 99%

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Coupling functions: Universal insights into dynamical interaction mechanisms

et al. 2017

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“…Decomposition of a coupling function can also facilitate a description of the functional contributions from each separate subsystem within the coupling relationship. Different methods for coupling function detection have been applied widely in chemistry [10,11,[14][15][16], in cardiorespiratory physiology [12,13,17], in neuroscience [18][19][20], in mechanical interactions [21], in social sciences [22] and in secure communications [23]. The study of coupling function is a very active and expanding field of research [24].…”

Section: Introductionmentioning

confidence: 99%

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Stankovski

2017

Phys. Rev. E

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Interactions in nature can be described by their coupling strength, direction of coupling and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems, however there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here -synchronization transition occurs only due to the time-variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brainwaves extracted from the electroencephalography (EEG) recording of a healthy human subject in a freerunning resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions, during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions and it should be taken into account when detecting biological or other interactions from data.

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“…Pikovsky [54]. Here, we select pairs of dissimilar oscillators (achieved via di↵erent applied voltages) from the whole population of 64.…”

Section: Notes To the Readermentioning

confidence: 99%

Improving Reduced Variable Models for Complex Systems via Experiment

Blaha

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Populations of simple interacting oscillators can give rise to complex dynamics.Real-world examples of such systems abound in biology, chemistry, and physics.Reduced-variable models can describe these systems. The phase model is a particularly successful reduced-variable model which, in its simplest form, each element is represented by one variable, the phase of oscillation. The phase model can be constructed from observable variables, without specific knowledge of underlying phenomenological behavior. Such reduced variable models are easier to construct and more generalizable than models derived from underlying physics or chemistry.In this dissertation, we study the dynamics of a population of coupled electrochemical oscillators in order to modify the phase model to expand its applicability.Specifically, we develop a two-phase model, a phase and radius model, and models with network coupling.We analyze data from two coupled oscillators with a standard one-dimensional phase model and a newer two-dimensional phase model. The same quantity of data is needed for either model. The two-dimensional analysis reveals behaviors and coupling parameters in theoretical and experimental examples that the onedimensional analysis does not show. The two-dimensional model could be useful in systems that exhibit learning due to its ability to distinguish stimulation and reaction. We extend the Stuart-Landau model to describe clustering dynamics for higher harmonic oscillators. We present examples of asymmetrical clusters arising from networks of higher harmonic oscillators. We show that the amplitude of oscillation is functionally influenced by coupling; we believe this "amplitude coupling function" has not been previously described. This function can be constructed from the original time series with no additional measurements.Recently, combined phase and amplitude models have gained attention; we explore the conditions where a phase and amplitude model is useful. We show experimentally a change in cluster state due only to changes in coupling strength. Such a transition is not possible with a phase-only model. Simulations with the extended Stuart-Landau model match experimental results. We demonstrate a method for predicting the amplitude coupling function from the coupling. Prior to this study, the relationship between stimulation and response was not known for the amplitude. We suggest that the phase and amplitude model will be most useful (1) in modeling high-harmonic oscillations, and (2) where coupling exceeds the "weak coupling" approximation of the phase-only model. iv

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Reconstruction of two-dimensional phase dynamics from experiments on coupled oscillators

Cited by 26 publications

References 31 publications

Coupling functions: Universal insights into dynamical interaction mechanisms

Coupling functions: Universal insights into dynamical interaction mechanisms

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Improving Reduced Variable Models for Complex Systems via Experiment

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