  The collective behavior in a population of globally coupled oscillators with
randomly distributed frequencies is studied when the natural frequency
distribution does not possess an even symmetry with respect to the average
natural frequency of oscillators. We study the special case of absence of
symmetry induced by a group of scaling transformations of the continuous
distribution of frequencies. When coupling between oscillators is increased
beyond a critical threshold favoring spontaneous synchronization, we found that
the variation in the velocity of the traveling wave depends on the extent of
asymmetry in the natural frequency distribution. In particular for large
coupling this velocity is the average natural frequency whereas at the onset of
synchronization it corresponds to the frequency where the Hilbert Transform of
the frequency distribution vanishes.

Adaptation and Self-Organizing Systems