Eur. Phys. J. B 69, 269-273 (2009)
https://doi.org/10.1140/epjb/e2009-00130-7

Interplay of noise and coupling in heterogeneous ensembles of phase oscillators

Consejo Nacional de Investigaciones Científicas y Técnicas, Centro Atómico Bariloche and Instituto Balseiro, 8400 Bariloche, Río Negro, Argentina

Corresponding author: ^a zanette@cab.cnea.gov.ar

Received: 23 January 2009
Revised: 11 March 2009
Published online: 15 April 2009

Abstract

We study the effects of noise on the collective dynamics of an ensemble of coupled phase oscillators whose natural frequencies are all identical, but whose coupling strengths are not the same all over the ensemble. The intensity of noise can also be heterogeneous, representing diversity in the individual responses to external fluctuations. We show that the desynchronization transition induced by noise may be completely suppressed, even for arbitrarily large noise intensities, is the distribution of coupling strengths decays slowly enough for large couplings. Equivalently, if the response to noise of a sufficiently large fraction of the ensemble is weak enough, desynchronization cannot occur. The two effects combine with each other when the response to noise and the coupling strength of each oscillator are correlated. This combination is quantitatively characterized and illustrated with explicit examples.