Probability of Stability of Synchronization in Random Networks of Mismatched Oscillators

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.