Nonlinear transient waves in coupled phase oscillators with inertia

Jörg, David J.

doi:10.1063/1.4919831

Cited by 10 publications

(14 citation statements)

References 45 publications

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“…Some representative ones are Refs. [48,49,50,51,52,53,54,55]. This review was entirely devoted to studies of mean-field interaction between the oscillators, namely, the case where every oscillator interacts with every other with a strength that is the same for every pair, thereby representing an extreme case of long-range interactions.…”

Section: Discussionmentioning

confidence: 99%

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Gherardini

Gupta

Ruffo

2018

Contemporary Physics

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Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously exhibit collective oscillations at a common frequency. The Kuramoto model provides the basic analytical framework to study spontaneous synchronization. The model comprises limit-cycle oscillators with distributed natural frequencies interacting through a mean-field coupling. Although more than forty years have passed since its introduction, the model continues to occupy the centre-stage of research in the field of non-linear dynamics, and is also widely applied to model diverse physical situations. In this brief review, starting with a derivation of the Kuramoto model and the synchronization phenomenon it exhibits, we summarize recent results on the study of a generalized Kuramoto model that includes inertial effects and stochastic noise. We describe the dynamics of the generalized model from a different yet a rather useful perspective, namely, that of long-range interacting systems driven out of equilibrium by quenched disordered external torques. A system is said to be long-range interacting if the inter-particle potential decays slowly as a function of distance. Using tools of statistical physics, we highlight the equilibrium and nonequilibrium aspects of the dynamics of the generalized Kuramoto model, and uncover a rather rich and complex phase diagram that it exhibits, which underlines the basic theme of intriguing emergent phenomena that are exhibited by many-body complex systems.

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Section: Discussionmentioning

confidence: 99%

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Gherardini

Gupta

Ruffo

2018

Contemporary Physics

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“…In a rapidly shortening tissue, the presence of gene expression waves results in a Doppler effect at the anterior end as the tissue boundary moves into the oncoming waves (Soroldoni et al., 2014, Jörg, 2015). In the same way that the pitch of a sound is higher for a moving observer approaching a source than a static observer at the source, the period with which gene expression waves arrive at the anterior end of the PSM has been experimentally shown to be shorter than the period with which they leave the posterior (Soroldoni et al., 2014).…”

Section: Wave Patterns and Their Influence From Delta-notch Signallingmentioning

confidence: 99%

“…For more details, we refer the reader to Jörg (2015). In summary, the output segmentation period observed at the anterior border of the PSM will depend on the period of oscillations set by the genetic feedback circuits visible in the posterior PSM, yet can be significantly modified by tissue-level contributions from wave effects.…”

Section: Wave Patterns and Their Influence From Delta-notch Signallingmentioning

confidence: 99%

“…In summary, the output segmentation period observed at the anterior border of the PSM will depend on the period of oscillations set by the genetic feedback circuits visible in the posterior PSM, yet can be significantly modified by tissue-level contributions from wave effects. Importantly, the magnitude of the Doppler contribution is determined by the velocity of tissue shortening and the wavelength of the wave pattern encountered at the anterior end of the PSM (Jörg, 2015). …”

Section: Wave Patterns and Their Influence From Delta-notch Signallingmentioning

confidence: 99%

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Delta-Notch signalling in segmentation

Liao

Oates

2017

Arthropod Structure & Development

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Modular body organization is found widely across multicellular organisms, and some of them form repetitive modular structures via the process of segmentation. It's vastly interesting to understand how these regularly repeated structures are robustly generated from the underlying noise in biomolecular interactions. Recent studies from arthropods reveal similarities in segmentation mechanisms with vertebrates, and raise the possibility that the three phylogenetic clades, annelids, arthropods and chordates, might share homology in this process from a bilaterian ancestor. Here, we discuss vertebrate segmentation with particular emphasis on the role of the Notch intercellular signalling pathway. We introduce vertebrate segmentation and Notch signalling, pointing out historical milestones, then describe existing models for the Notch pathway in the synchronization of noisy neighbouring oscillators, and a new role in the modulation of gene expression wave patterns. We ask what functions Notch signalling may have in arthropod segmentation and explore the relationship between Notch-mediated lateral inhibition and synchronization. Finally, we propose open questions and technical challenges to guide future investigations into Notch signalling in segmentation.

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“…Furthermore, each new somite consisted of the anteriormost cells that contained 21% of the total phase difference across the PSM, irrespective of the length of the PSM at that time [4]. Although many different aspects of the coupled oscillating cells in the PSM have been investigated theoretically, ranging from models of global wave patterns and morphogen gradients, to models of the underlying biological clocks, and the effect of couplings on defect-free patterning [8,[10][11][12][13][14][15][16][17][18][19][20], nothing is known about the measurable consequences of such phenomenological observations about the phase of the cells in the PSM. In the present paper, this is what we seek to illuminate.…”

Section: Introductionmentioning

confidence: 99%

Constraints on somite formation in developing embryos

Juul

Jensen

Krishna

2019

Preprint

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Segment formation in vertebrate embryos is a stunning example of biological self-organisation. Here, we present an idealized model of the presomitic mesoderm (PSM) as a one-dimensional line of oscillators. We use the model to derive constraints that connect the size of somites, and the timing of their formation, to the growth of the PSM and the gradient of the somitogenesis clock period across the PSM. Our analysis recapitulates the observations made recently in ex-vivo cultures of mouse PSM cells, and makes predictions for how perturbations, such as increased Wnt levels, would alter somite widths. Finally, our model makes testable predictions for the shape of the phase profile and somite widths at different stages of PSM growth. In particular, we show that the phase profile is robustly concave when the PSM length is steady and slightly convex in an important special case when it is decreasing exponentially. In both cases, the phase profile scales with the PSM length; in the latter case, it scales dynamically. This has important consequences for the velocity of the waves that traverse the PSM and trigger somite formation, as well as the effect of errors in phase measurement on somite widths.

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Nonlinear transient waves in coupled phase oscillators with inertia

Cited by 10 publications

References 45 publications

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Spontaneous synchronisation and nonequilibrium statistical mechanics of coupled phase oscillators

Delta-Notch signalling in segmentation

Constraints on somite formation in developing embryos

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