Network topology plays an important role in governing the collective dynamics. Partial synchronization (PaS) on regular networks with a few non-local links is explored. Different PaS patterns out of the symmetry breaking are observed for different ways of non-local couplings. The criterion for the emergence of PaS is studied. The emergence of PaS is related to the loss of degeneration in Lyapunov exponent spectrum. Theoretical and numerical analysis indicate that non-local coupling may drastically change the dynamical feature of the network, emphasizing the important topological dependence of collective dynamics on complex networks.
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