Synchronizability via Pinning Control on Multi-Weighted Complex Dynamical Networks

This paper analyzes synchronization performances and formulates synchronizability criteria for multi-weighted complex dynamical networks under pinning control. General synchronization conditions and a pinning controller design method are derived. On this basis, synchronizability criteria are established by analyzing the effects of network topology and coupling strength on pinning synchronization. Furthermore, a synchronizability criterion is derived based on the eigenvalues at the unpinned nodes, which takes into account multiple attributes and effectively reduces the global computational complexity as the number of pinned nodes is varied or the pinning strategy is adjusted. Finally, under the proposed synchronizability criteria, this paper systematically analyzes the impact of key parameters on the synchronizability of multi-weighted BA and NW networks. Experimental results demonstrate that pinning high-degree nodes is more effective when the number of pinned nodes is small, whereas pinning low-degree nodes becomes more advantageous as the number of pinned nodes increases, for both multi-weighted BA and NW networks. For multi-weighted NW networks, the edge-addition probability not only affects the network synchronizability but also plays a key role in determining the critical number of nodes for pinning strategies. This study reveals the significant influence of multiple weight attributes, total in-degree of nodes, and coupling structures on the synchronizability of multi-weighted networks under pinning control, offering valuable insights in optimizing pinning strategies for improving the network synchronizability.