Synchronization dynamics of mobile oscillators in the presence of coupling delays

Gabriela Petrungaro, Koichiro Uriu, and Luis G. Morelli
Phys. Rev. E 99, 062207 – Published 10 June 2019

Abstract

Individual biological oscillators can synchronize to generate a collective rhythm. During vertebrate development, mobile cells exchange signals to synchronize a rhythmic pattern generator that makes the embryonic segments. Previous theoretical works have shown that cell mobility can enhance synchronization of coupled oscillators when signal exchange is instantaneous. However, in vertebrate segmentation, the exchange of signals is thought to comprise delays from signal sending and processing, which could alter the effect of mobility on synchronization. Here, we study synchronization dynamics of mobile phase oscillators in the presence of coupling delays. We find that mobility can speed up synchronization when coupling delays are present. We derive an analytical expression for the characteristic time of synchronization dynamics, which is in very good agreement with numerical simulations. This analytical expression suggests a subdivision of the mobility range into different dynamical regimes and reveals that, with delayed coupling, synchronization is enhanced at a lower mobility rate than with instantaneous coupling. We argue that these results may be relevant to the synchronization of mobile oscillators in vertebrate segmentation.

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  • Received 31 January 2019

DOI:https://doi.org/10.1103/PhysRevE.99.062207

©2019 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsNonlinear Dynamics

Authors & Affiliations

Gabriela Petrungaro1,2,3, Koichiro Uriu4,*, and Luis G. Morelli1,2,5,†

  • 1Instituto de Investigación en Biomedicina de Buenos Aires (IBioBA)–CONICET–Partner Institute of the Max Planck Society, Polo Científico Tecnológico, Godoy Cruz 2390, C1425FQD, Buenos Aires, Argentina
  • 2Departamento de Física, FCEyN UBA, Ciudad Universitaria, 1428 Buenos Aires, Argentina
  • 3Institute for Biological Physics, University of Cologne, Zülpicher Strasse 47a, 50674 Köln, Germany
  • 4Graduate School of Natural Science and Technology, Kanazawa University, Kakuma-machi, Kanazawa 920-1192, Japan
  • 5Max Planck Institute for Molecular Physiology, Department of Systemic Cell Biology, Otto-Hahn-Strasse 11, D-44227 Dortmund, Germany

  • *uriu@staff.kanazawa-u.ac.jp
  • morelli@df.uba.ar

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Issue

Vol. 99, Iss. 6 — June 2019

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