  We investigate the combined effects of distributed delay and the balance
between excitatory and inhibitory nodes on the stability of synchronous
oscillations in a network of coupled Stuart--Landau oscillators. To this end a
network model is proposed for which the stability can be investigated
analytically. It is found that beyond a critical inhibition ratio
synchronization tends to be unstable. However, increasing distributional widths
can counteract this trend leading to multiple resynchronization transitions at
relatively high inhibition ratios. All studies are performed on two
distribution types, a uniform distribution and a Gamma distribution.
