Spectral universality of phase synchronization in non-identical oscillator networks |
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Authors: | N Fujiwara and J Kurths |
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Institution: | (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 |
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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. |
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Keywords: | PACS" target="_blank">PACS 05 45 Xt Synchronization coupled oscillators 89 75 Hc Networks and genealogical trees |
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