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.

We investigate the synchronization of stochastic multiple weighted coupled networks with Markovian switching (SMWCNMS). By designing an appropriate controller, we obtain several sufficient criteria ensuring the pth moment exponential synchronization and almost surely exponential synchronization for SMWCNMS based on graph theory. Moreover, we also investigate the pth moment asymptotical synchronization and almost surely asymptotical synchronization for SMWCNMS. Finally, we provide a numerical example to illustrate the availability of the proposed synchronization criteria.

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In this paper, the partial topology identification of stochastic multi-group models with multiple dispersals is investigated. Based on adaptive pinning control and a graph-theoretic method, some sufficient criteria about partial topology identification of stochastic multi-group models with multiple dispersals are obtained. That is to say, the unknown partial topological structures can be identified successfully. In the end, numerical examples are provided to verify the effectiveness of theoretical results.