Eur. Phys. J. B 69, 45-49 (2009)
https://doi.org/10.1140/epjb/e2009-00078-6

Spectral universality of phase synchronization in non-identical oscillator networks

¹ Center for Dynamics of Complex Systems, University of Potsdam, 14415 Potsdam, Germany
² Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
³ Department of Physics, Humboldt University Berlin, 12489 Berlin, Germany

Corresponding author: ^a naoya-f@ams.odn.ne.jp

Received: 28 November 2008
Revised: 4 February 2009
Published online: 3 March 2009

Abstract

We employ a spectral decomposition method to analyze synchronization of a non-identical oscillator network. We study the case that a small parameter mismatch of oscillators is characterized by one parameter and phase synchronization is observed. We derive a linearized equation for each eigenmode of the coupling matrix. The parameter mismatch is reflected on inhomogeneous term in the linearized equation. We find that the oscillation of each mode is essentially characterized only by the eigenvalue of the coupling matrix with a suitable normalization. We refer to this property as spectral universality, because it is observed irrespective of network topology. Numerical results in various network topologies show good agreement with those based on linearized equation. This universality is also observed in a system driven by additive independent Gaussian noise.