  Systems that synchronize in nature are intrinsically different from one
another, with possibly large differences from system to system. While a vast
part of the literature has investigated the emergence of network
synchronization for the case of small parametric mismatches, we consider the
general case that parameter mismatches may be large. We present a unified
stability analysis that predicts why the range of stability of the synchronous
solution either increases or decreases with parameter heterogeneity for a given
network. We introduce a parametric approach, based on the definition of a
curvature contribution function, which allows us to estimate the effect of
mismatches on the stability of the synchronous solution in terms of
contributions of pairs of eigenvalues of the Laplacian. For cases in which
synchronization occurs in a bounded interval of a parameter, we study the
effects of parameter heterogeneity on both transitions (asynchronous to
synchronous and synchronous to asynchronous.)
