Self-averaging of an order parameter in randomly coupled limit-cycle oscillators
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.
Stiller
JC
Institut fur Biologie III, Universitat Freiburg, and AG Hirnforschung, Hansastrasse 9a, D-79104 Freiburg, Germany.
Radons
G