Abstract
In this paper, we systematically investigate the stability issues of different kinds of collective behaviors, including the equilibrium point, complete synchronization, quenched hub incoherence, anti-phase remote synchronization and regular remote synchronization, which arise in identical Stuart–Landau oscillators asymmetrically coupled in a star network. We have analytically obtained their rigorous stability conditions and stable basins, which are well verified by numerical results. Additionally, we surprisingly find that, for measuring the remote synchronization, the two traditional order parameters rdirect and rindirect are not well-defined metrics. All these results may help us to further improve our understanding of nonlinear systems’ complete, partial and cluster synchronization behaviors in real or man-made complex networks.
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