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The European Physical Journal Special Topics

, Volume 227, Issue 10–11, pp 1117–1128 | Cite as

Desynchronization by phase slip patterns in networks of pulse-coupled oscillators with delays

Desynchronization by phase slip patterns
  • Vladimir KlinshovEmail author
  • Leonhard Lücken
  • Serhiy Yanchuk
Regular Article
Part of the following topical collections:
  1. Advances in Nonlinear Dynamics of Complex Networks: Adaptivity, Stochasticity, Delays

Abstract

Coupling delays may cause drastic changes in the dynamics of oscillatory networks. In the present paper we investigate how coupling delays alter synchronization processes in networks of all-to-all coupled pulse oscillators. We derive an analytic criterion for the stability of synchrony and study the synchronization areas in the space of the delay and coupling strength. Specific attention is paid to the scenario of destabilization on the borders of the synchronization area. We show that in bifurcation points the system possesses homoclinic loops, which give rise to complex long- or quasi-periodic solutions. These newly born solutions are characterized by a synchronous group, from which an oscillator periodically escapes, laps one period, and rejoins. We call such a dynamical regime “phase slip patterns”.

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Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Vladimir Klinshov
    • 1
    Email author
  • Leonhard Lücken
    • 2
  • Serhiy Yanchuk
    • 3
  1. 1.Institute of Applied Physics of the Russian Academy of SciencesNizhny NovgorodRussia
  2. 2.German Aerospace Center (DLR), Institute of Transportation SystemsBerlinGermany
  3. 3.Technical University of Berlin, Institute of MathematicsBerlinGermany

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