  The Kuramoto model has provided deep insights into synchronization phenomena
and remains an important paradigm to study the dynamics of coupled oscillators.
Yet, despite its success, the asynchronous regime in the Kuramoto model has
received limited attention. Here, we adapt and enhance the mean-field approach
originally proposed by Stiller and Radons [Phys. Rev. E 58 (1998)] to study the
asynchronous state in the Kuramoto model with a finite number of oscillators
and with disordered connectivity. By employing an iterative stochastic mean
field (IMF) approximation, the complex N-oscillator system can effectively be
reduced to a one-dimensional dynamics, both for homogeneous and heterogeneous
networks. This method allows us to investigate the power spectra of individual
oscillators as well as of the multiplicative "network noise" in the Kuramoto
model in the asynchronous regime. By taking into account the finite system size
and disorder in the connectivity, our findings become relevant for the dynamics
of coupled oscillators that appear in the context of biological or technical
systems.
