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We derive a master stability function (MSF) for synchronization in networksof coupled dynamical systems with small but arbitrary parametric variations.Analogous to the MSF for identical systems, our generalized MSF simultaneouslysolves the linear stability problem for near-synchronous states (NSS) for allpossible connectivity structures. We also derive a general sufficient conditionfor stable near-synchronization and show that the synchronization error scaleslinearly with the magnitude of parameter variations.Our analysis underlinessignificant roles played by the Laplacian eigenvectors in the study of networksynchronization of near-identical systems.

Master Stability Functions for Coupled Near-Identical Dynamical Systems