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 deviati ons from a power-law decay for the "magnetization" of a system of coupled p hase oscillators with random interactions claimed by Daido in Phys. Rev. Le tt. 68, 1072 (1992). For another long-time property, the Lyaponov exponent, we found that his numerical procedure showed strong time discretization ef fects and we suspected a similar effect for the algebraic decay. In the Com ment to our paper [preceding paper, Phys. Rev. E 61, 2145 (2000)] Daido mad e clear that the power law behavior was only claimed for the sample average d magnetization [Z] and he presented new, more accurate numerical results w hich 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 t aken the intrinsic oscillator frequencies as Gaussian random variables, whi le Daido in his new and apparently also in his earlier simulations used a d eterministic approximation to the Gaussian distribution; Due to the differe nces in the observed quantity and the model assumptions our and Daido's res ults may be compatible.