The \(L_p\) metric-based synchronization problem of memristor-based neural networks (MNNs) with multiple links and multiple leakage delays (ML-MLDs) is investigated. Firstly, to guarantee \(L_p\) metric-based synchronization between the drive and response MNNs with ML-MLDs, a novel controller is created. Secondly, a novel criterion of \(L_p\) metric-based synchronization is obtained via a property of solutions of the error system. This proposed method eliminates the need for Lyapunov–Krasovskii functional (LKF), which can result in simpler synchronization criterion than the existing ones, and thereby it is easy to check. Finally, numerical examples are provided to illustrate the feasibility of the derived \(L_p\) metric-based synchronization criterion and its advantages over the existing ones. These findings are crucial for advancing secure communication, biological network modeling, and other applications. It should be noted specially that the \(L_p\) metric-based synchronization problem of MNNs with ML-MLDs is solved for the first time.
