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

Stankovski, Tomislav

doi:10.1103/physreve.95.022206

Cited by 19 publications

(15 citation statements)

References 65 publications

(98 reference statements)

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“…Applications could be especially enticing in brain dynamics, where neural cross-frequency coupling functions have been derived [32]. In this example, one challenge is that the coupling function can exhibit time dependence [71]. Theoretical development is needed to better characterize experiment-based phase models; promising approaches include the introduction of amplitude dependence [72] or factoring in slow relaxation processes resulting in changes in natural frequencies [73].…”

Section: Resultsmentioning

confidence: 99%

Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

Šebek

Kawamura

Nott

et al. 2019

Phil. Trans. R. Soc. A.

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The synchronization of two groups of electrochemical oscillators is investigated during the electrodissolution of nickel in sulfuric acid. The oscillations are coupled through combined capacitance and resistance, so that in a single pair of oscillators (nearly) in-phase synchronization is obtained. The internal coupling within each group is relatively strong, but there is a phase difference between the fast and slow oscillators. The external coupling between the two groups is weak. The experiments show that the two groups can exhibit (nearly) anti-phase collective synchronization. Such synchronization occurs only when the external coupling is weak, and the interactions are delayed by the capacitance. When the external coupling is restricted to those between the fast and the slow elements, the anti-phase synchronization is more prominent. The results are interpreted with phase models. The theory predicts that, for anti-phase collective synchronization, there must be a minimum internal phase difference for a given shift in the phase coupling function. This condition is less stringent with external fast-to-slow coupling. The results provide a framework for applications of collective phase synchronization in modular networks where weak coupling between the groups can induce synchronization without rearrangements of the phase dynamics within the groups. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

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Section: Resultsmentioning

confidence: 99%

Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

Šebek

Kawamura

Nott

et al. 2019

Phil. Trans. R. Soc. A.

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“…The time-varying form of the coupling functions (Figure 6) can be a cause of self-organization transitions, like the emergence of network clustering, or of the systems going into-and-out-of synchronization (Stefanovska et al, 2000; Varela et al, 2001), even for an invariant net coupling strength (Stankovski, 2017). More importantly, having detected and characterized a neural coupling function, one can then use this knowledge to detect, or even to predict, the onset of phase synchronization (Kiss et al, 2005).…”

Section: Discussionmentioning

confidence: 99%

Neural Cross-Frequency Coupling Functions

Stankovski

Ticcinelli

McClintock

et al. 2017

Front. Syst. Neurosci.

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Although neural interactions are usually characterized only by their coupling strength and directionality, there is often a need to go beyond this by establishing the functional mechanisms of the interaction. We introduce the use of dynamical Bayesian inference for estimation of the coupling functions of neural oscillations in the presence of noise. By grouping the partial functional contributions, the coupling is decomposed into its functional components and its most important characteristics—strength and form—are quantified. The method is applied to characterize the δ-to-α phase-to-phase neural coupling functions from electroencephalographic (EEG) data of the human resting state, and the differences that arise when the eyes are either open (EO) or closed (EC) are evaluated. The δ-to-α phase-to-phase coupling functions were reconstructed, quantified, compared, and followed as they evolved in time. Using phase-shuffled surrogates to test for significance, we show how the strength of the direct coupling, and the similarity and variability of the coupling functions, characterize the EO and EC states for different regions of the brain. We confirm an earlier observation that the direct coupling is stronger during EC, and we show for the first time that the coupling function is significantly less variable. Given the current understanding of the effects of e.g., aging and dementia on δ-waves, as well as the effect of cognitive and emotional tasks on α-waves, one may expect that new insights into the neural mechanisms underlying certain diseases will be obtained from studies of coupling functions. In principle, any pair of coupled oscillations could be studied in the same way as those shown here.

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“…From the previous section, the net coupling strength of the master-slave configuration q t in equation (5.1) can be defined as ∥qt∥2=αfalse(tfalse)=12c12(t)+c22(t),where c 1 ( t ) and c 2 ( t ) are the time-varying coupling parameters of the coupling functions [23]. In the autonomous case, where the coupling parameters c 1 and c 2 are constant, if the net coupling strength ∥q∥2=α>12|ω1−ω2| then the oscillators will synchronize [23]. In the present study, unlike the autonomous case, the oscillators are not guaranteed to be synchronized all of the time.…”

Section: Numericsmentioning

confidence: 99%

Synchronization transitions caused by time-varying coupling functions

Hagos

Stankovski

Newman

et al. 2019

Phil. Trans. R. Soc. A.

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Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable.This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

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

Cited by 19 publications

References 65 publications

Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

Anti-phase collective synchronization with intrinsic in-phase coupling of two groups of electrochemical oscillators

Neural Cross-Frequency Coupling Functions

Synchronization transitions caused by time-varying coupling functions

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