  The stability of synchronization state in networks of oscillators are studied
under the assumption that oscillators and their couplings have slightly
mismatched parameters. A generalized master stability function is provided that
takes the mismatches into account. Using this master stability function a lower
bound on the probability of synchronization is derived for regular and random
network models. The probability of stability of synchronization is then used to
study the phase transition behavior of the networks. Numerical examples using
van der Pol oscillators are used to illustrate the results and verify the
validity of the analysis. Moreover, the synchronization trend as a function of
statistics of mismatches in the coupling and local dynamics is investigated
using this numerical example.
