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Desynchronization and Chaos in the Kuramoto Model

  • Y.L. Maistrenko
  • O.V. Popovych
  • P.A. Tass
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 671)

Abstract

Abstract. The Kuramoto model of N globally coupled phase oscillators is an essentially non-linear dynamical system with a rich dynamical behavior and a high relevance for numerous applications. We study the Kuramoto model from the standpoint of bifurcation theory and chaos theory of low-dimensional dynamical systems. We focus on the desynchronization transition and the role of the Cherry flow in it. Furthermore, we study chaos, hyperchaos, and multistability. With an additional symmetry condition the Kuramoto model is reduced to the Winfree type model of half the dimension. We find out that the dynamics in the symmetric manifold is responsible for the desynchronization transition. With a further decrease of the coupling, the manifold loses its transverse stability, which gives rise to a highly developed hyperchaotic behavior.

Keywords

Lyapunov Exponent Deep Brain Stimulation Invariant Manifold Chaotic Attractor Phase Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • Y.L. Maistrenko
    • 1
    • 2
    • 4
  • O.V. Popovych
    • 1
    • 4
  • P.A. Tass
    • 1
    • 3
  1. 1.Institute of MedicineResearch Centre JülichGermany
  2. 2.Central Institute for ElectronicsResearch Center JülichGermany
  3. 3.Department of Stereotaxic and Functional NeurosurgeryUniversity HospitalGermany
  4. 4.Institute of MathematicsAcademy of Sciences of UkraineUkraine

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