  The self-consistent method, first introduced by Kuramoto, is a powerful tool
for the analysis of the steady states of coupled oscillator networks. For
second-order oscillator networks complications to the application of the
self-consistent method arise because of the bistable behavior due to the
co-existence of a stable fixed point and a stable limit cycle, and the
resulting complicated boundary between the corresponding basins of attraction.
In this paper, we report on a self-consistent analysis of second-order
oscillators which is simpler compared to previous approaches while giving more
accurate results in the small inertia regime and close to incoherence. We apply
the method to analyze the steady states of coupled second-order oscillators and
we introduce the concepts of margin region and scaled inertia. The improved
accuracy of the self-consistent method close to incoherence leads to an
accurate estimate of the critical coupling corresponding to transitions from
incoherence.
