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Approximate cluster synchronization in networks with symmetries and parameter mismatches
L. M. Pecora, F. Sorrentino, A. M. Hagerstrom, T. E. Murphy, and R. Roy, “ Cluster synchronization and isolated desynchronization in complex networks with symmetries,” Nat. Commun. 5, 4079 (2014).
F. Sorrentino, L. M. Pecora, A. M. Hagerstrom, T. E. Murphy, and R. Roy, “ Complete characterization of stability of cluster synchronization in complex dynamical networks,” Sci. Adv. 2, e1501737 (2016).
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We study cluster synchronization in networks with symmetries in the presence of small generic parametric mismatches of two different types: mismatches affecting the dynamics of the individual uncoupled systems and mismatches affecting the network couplings. We perform a stability
analysis of the nearly synchronous cluster synchronization solution and reduce the stability problem to a low-dimensional form. We also show how under certain conditions the low dimensional analysis can be used to predict the overall synchronization error, i.e., how close the individual nearly synchronous trajectories are to each other.
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