  Chaotic systems can be synchronized by linking them to a common signal,
subject to certain conditions. However, the presence of multiple driving
signals coming from different systems, give rise to novel behavior. The
particular case of Lorenz systems, with two independent systems driving another
system through drive-response coupling has been studied in this paper. This is
the simplest arrangement which shows the effect of ``frustrated
synchronization'' due to competition between the two driver systems. The
resulting response system attractor deviates significantly from the
conventional Lorenz attractor. A new measure of desynchronization is proposed,
which shows a power-law scaling with the competition parameter.
