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

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