Eigenvalue based approach to pinning synchronization in general coupled networks

The synchronization in general coupled networks forced by pinning control is investigated based on eigenvalue analysis. The stable regions for different types of inner coupling links are obtained and the eigenvalue distributions of the coupling and control matrices are analyzed. The effects of network size, weight value of edges, pinning density and pinning strength on the network stability are also tested in numerical studies. It is found that the pinning stability can be improved via increasing the weight of the edges, pinning density and pinning strength for types (i), (iii) and (iv) stable regions, whereas for type (ii) critical curve, too large pinning density and pinning strength will break stable synchronous state.