Accelerating Synchronization via Edge-Addition or Edge-Removal in a Chaotic Directed Network

Synchronizability is characterized by the smallest real part of the nonzero Laplacian eigenvalues, known as algebraic connectivity. It is known that adding edges is an effective strategy for improving network synchronizability in undirected networks. A natural question is, does this conclusion also hold for directed networks? This paper aims to answer this question. Utilizing Laplacian eigenvectors, an approach focusing on accelerating synchronization of directed networks through edge-addition or edge-removal is proposed by providing an approximate variation in algebraic connectivity. The greater the approximate variation of an edge, the more advantageous regarding synchronizability it is to add or remove that edge. Further, we identify the optimal edge with a fixed node as the head to improve network synchronizability. To validate the effectiveness of our theory, we analyze a seven-node toy network with chaotic Chua’s circuits as the node dynamics and simulate a large-scale real mouse brain real network. By integrating network dynamics with edge-addition or edge-removal, this paper offers valuable insights for selecting appropriate edges to accelerate synchronization in directed networks.