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Self-averaging of an order parameter in randomly coupled limit-cycle oscillators

Selbstermittlung eines Ordnungsparameters bei zufällig gekoppelten Grenz-Zyklus-Oszillatoren
: Stiller, J.C.; Radons, G.


Physical Review. E 61 (2000), No.2, pp.2148-2149
ISSN: 1063-651X
ISSN: 1539-3755
Journal Article
Fraunhofer IPA ()
Nichtlineare Dynamik; Ungeordnetes System; Gekoppelter Oszillator; Phasenoszillator; Ordnungsparameter; Selbstmitteilung; Coupled Oscillator system; Disordered Systems; Nonlinear Dynamics; Phase Oscillator; Order Parameter; Self-Averaging; Dynamik

In our recent paper (Phys. Rev. E 58, 1789 (1998)) we found notable deviations from a power-law decay for the "magnetization" of a system of coupled phase oscillators with random interactions claimed by Daido in Phys. Rev. Lett. 68, 1072 (1992). For another long-time property, the Lyaponov exponent, we found that his numerical procedure showed strong time discretization effects and we suspected a similar effect for the algebraic decay. In the Comment to our paper (preceding paper, Phys. Rev. E 61, 2145 (2000)) Daido made clear that the power law behavior was only claimed for the sample averaged magnetization [Z] and he presented new, more accurate numerical results which provide evidence for a power-law decay of this quantity. Our results, however, were obtained for Z itself and not for [Z]. In addition, we have taken the intrinsic oscillator frequencies as Gaussian random variables, while Daido in his new and apparently also in his earlier simulations used a deterministic approximation to the Gaussian distribution. Due to the differences in the observed quantity and the model assumptions our and Daido's results may be compatible.