Complete synchronization and stability of star-shaped complex networks (Q813667)

The authors study the synchronization of three different cases of star-shaped map coupled networks using linear stability analysis. They found that the star-shaped networks of \(N\) modes with one or \(K\)-center nodes \((K\ll N)\) in which all noncenter nodes connect to every center node only can achieve stable synchronization for some coupling strength \(\varepsilon\) as \(0,5<\varepsilon <0,75\) when \(N\) sufficiently large. On the other hand, for the star-shaped network of \(k\) center nodes with each center connecting to \(n\) different non-center nodes should satisfy the condition \(k\geq 3n+1\) in order to synchronize stably, and the range of coupling strength depends on \(k\) and \(n\).