Topology identification of multi‐weighted complex networks based on adaptive synchronization: A graph‐theoretic approach

This paper aims to identify the topological structures of multi‐weighted complex networks (MWCN) with and without time delay based on adaptive synchronization. First, by using the concept of drive‐response synchronization, one takes the MWCN as a drive system and introduces the adaptive controller and white noise in the response system to get stochastic MWCN. Then, drive system and response system achieve synchronization by combining graph theory, Lyapunov stability theory, and adaptive control technique. At the same time, the uncertain multiple topological structures of drive system can be identified by response system based on adaptive synchronization. Furthermore, topological structures of MWCN with time delay are also successfully identified. Finally, numerical simulations for the identification of coupled chaotic systems are provided to verify the effectiveness of theoretical results.