  We adapt a previous model and analysis method (the {\it master stability
function}), extensively used for studying the stability of the synchronous
state of networks of identical chaotic oscillators, to the case of oscillators
that are similar but not exactly identical. We find that bubbling induced
desynchronization bursts occur for some parameter values. These bursts have
spatial patterns, which can be predicted from the network connectivity matrix
and the unstable periodic orbits embedded in the attractor. We test the
analysis of bursts by comparison with numerical experiments. In the case that
no bursting occurs, we discuss the deviations from the exactly synchronous
state caused by the mismatch between oscillators.
