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.

中文翻译：

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基于自适应同步的多加权复杂网络拓扑识别：一种图论方法

本文旨在基于自适应同步来确定具有和不具有时间延迟的多加权复杂网络（MWCN）的拓扑结构。首先，通过使用驱动响应同步的概念，将MWCN作为驱动系统，并在响应系统中引入自适应控制器和白噪声，以获得随机MWCN。然后，驱动系统和响应系统通过结合图论，李雅普诺夫稳定性理论和自适应控制技术实现同步。同时，基于自适应同步的响应系统可以识别驱动系统的不确定的多种拓扑结构。此外，还成功地确定了具有时间延迟的MWCN的拓扑结构。最后，