Phase synchronization between collective rhythms of fully locked oscillator groups

Kawamura, Y.

doi:10.1038/srep04832

Cited by 15 publications

(16 citation statements)

References 65 publications

(154 reference statements)

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“…Synchronization and its quantification has been widely discussed in networks of coupled oscillators [43][44][45][46]. Our hope is that these set of studies contributes to an already diverse set of work and adds to understanding of the impact of ion channel behaviors as well as coupling in the SAN pacemaker.…”

Section: Discussionmentioning

confidence: 99%

Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

et al. 2018

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Computational studies using mathematical models of the sinoatrial node (SAN) cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, cardiac arrhythmias, and potential therapies. While the impact of ion channel dynamics on SAN pacemaking has been studied, the governing dynamics responsible for regulating spatial and temporal control of SAN synchrony remain elusive. Here, we attempt to develop methods to explore cohesion in a network of coupled spontaneously active SAN cells. We present the updated version of a previously published graphical user interface LongQt: a cross-platform, threaded application for advanced cardiac electrophysiology studies that does not require advanced programming skills. We incorporated additional features to the existing LongQt platform that allows users to (1) specify heterogeneous gap junction conductivity across a multicellular grid, and (2) set heterogeneous ion channel conductance across a multicellular grid. We developed two methods of characterizing the synchrony of SAN tissue based on alignment of activation in time and similarity of voltage peaks among clusters of functionally related cells. In pairs and two-dimensional grids of coupled cells, we observed a range of conductivities (0.00014-0.00033 1/ -cm) in which the tissue was more susceptible to developing asynchronous spontaneous pro-arrhythmic behavior (e.g., spiral wave formation). We performed parameter sensitivity analysis to determine the relative impact of ion channel conductances on cycle length (CL), diastolic and peak voltage, and synchrony measurements in isolated and coupled cell pairs. We also defined measurements of evaluating synchrony based on peak AP voltage and the rate of wave propagation. Cell-to-cell coupling had a non-linear effect on the relationship between ion channel conductances, AP properties, and synchrony measurements. Our simulations demonstrate that conductivity plays an important role in regulating synchronous firing of heterogeneous SAN tissue, and demonstrate how to evaluate the role of coupling and ion channel conductance in pairs and grids of SAN cells. We anticipate that the approach outlined here will facilitate identification of key cell-and tissue-level factors responsible for cardiac disease.

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Section: Discussionmentioning

confidence: 99%

Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

et al. 2018

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“…where the centroids B, P 1 and P 2 of each of the three populations are defined by the average of β i and the two groups of ρ i in B, R 1 and R 2 . Correspondingly, the central quantities of interest in this regime are the difference between each network's centroid 28) and the quantity α BR 2 is given as the following linear sum,…”

Section: The Case Of Three Clusters: Fragmentation Of Redmentioning

confidence: 99%

“…Such phenomena has been observed elsewhere [24,25,26] but to our knowledge this is the first example of this arising from noise in a multi-network Kuramoto based system. Our 'Blue-vs-Red' formalism is a special case of that of [27,28] though we additionally apply noise, and provide numerical illustrations of larger more complex systems.…”

Section: Introductionmentioning

confidence: 99%

Gaussian noise and the two-network frustrated Kuramoto model

Holder

Zuparic

Kalloniatis

2017

Physica D: Nonlinear Phenomena

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We examine analytically and numerically a variant of the stochastic Kuramoto model for phase oscillators coupled on a general network. Two populations of phased oscillators are considered, labelled `Blue' and `Red', each with their respective networks, internal and external couplings, natural frequencies, and frustration parameters in the dynamical interactions of the phases. We disentagle the different ways that additive Gaussian noise may influence the dynamics by applying it separately on zero modes or normal modes corresponding to a Laplacian decomposition for the sub-graphs for Blue and Red. Under the linearisation ansatz that the oscillators of each respective network remain relatively phase-sychronised centroids or clusters, we are able to obtain simple closed-form expressions using the Fokker-Planck approach for the dynamics of the average angle of the two centroids. In some cases, this leads to subtle effects of metastability that we may analytically describe using the theory of ratchet potentials. These considerations are extended to a regime where one of the populations has fragmented in two. The analytic expressions we derive largely predict the dynamics of the non-linear system seen in numerical simulation. In particular, we find that noise acting on a more tightly coupled population allows for improved synchronisation of the other population where deterministically it is fragmented.Comment: 55 pages, 17 figures, accepted by Physica

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“…Generalization of the phase reduction method for highdimensional systems exhibiting collective oscillations has recently been developed for coupled phase oscillators with global coupling [18] and with general network coupling [19], and for active rotators with global coupling [20]. Similar idea has been applied for the analysis of mutual synchronization between collectively oscillating populations of coupled phase oscillators [21][22][23]. Moreover, the idea of collective phase reduction has further been generalized to spatially extended systems such as thermal convection [24,25] and reaction-diffusion systems exhibiting rhythmic spatio-temporal dynamics [26].…”

Section: Introductionmentioning

confidence: 99%

Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations

Nakao

Yasui

Ota

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A general phase reduction method for a network of coupled dynamical elements exhibiting collective oscillations, which is applicable to arbitrary networks of heterogeneous dynamical elements, is developed. A set of coupled adjoint equations for phase sensitivity functions, which characterize phase response of the collective oscillation to small perturbations applied to individual elements, is derived. Using the phase sensitivity functions, collective oscillation of the network under weak perturbation can be described approximately by a one-dimensional phase equation. As an example, mutual synchronization between a pair of collectively oscillating networks of excitable and oscillatory FitzHugh-Nagumo elements with random coupling is studied.Networks of coupled dynamical elements exhibiting collective oscillations often play important functional roles in real-world systems. Here, a method for dimensionality reduction of such networks is proposed by extending the classical phase reduction method for nonlinear oscillators. By projecting the network state to a single phase variable, a simple one-dimensional phase equation describing the collective oscillation is derived. As an example, synchronization between collectively oscillating random networks of neural oscillators is studied. The derived phase equation is general and will have wide applicability in control and optimization of collectively oscillating networks.

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Phase synchronization between collective rhythms of fully locked oscillator groups

Cited by 15 publications

References 65 publications

Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

Gaussian noise and the two-network frustrated Kuramoto model

Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations

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