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Perturbation analysis of complete synchronization in networks of phase oscillators

Ralf Tönjes1,2 and Bernd Blasius3

  • 1Institut für Physik, Universität Potsdam, 14415 Potsdam, Germany
  • 2Ochadai Academic Production, Ochanomizu University, Tokyo 112-8610, Japan
  • 3ICBM, University Oldenburg, 26111 Oldenburg, Germany

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Phys. Rev. E 80, 026202 – Published 10 August, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.026202

Abstract

The behavior of weakly coupled self-sustained oscillators can often be well described by phase equations. Here we use the paradigm of Kuramoto phase oscillators which are coupled in a network to calculate first- and second-order corrections to the frequency of the fully synchronized state for nonidentical oscillators. The topology of the underlying coupling network is reflected in the eigenvalues and eigenvectors of the network Laplacian which influence the synchronization frequency in a particular way. They characterize the importance of nodes in a network and the relations between them. Expected values for the synchronization frequency are obtained for oscillators with quenched random frequencies on a class of scale-free random networks and for a Erdös-Rényi random network. We briefly discuss an application of the perturbation theory in the second order to network structural analysis.

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Phys. Rev. E 80, 026202– Published 10 August, 2009
  • Received 1 May 2009

© 2009 American Physical Society

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