Synchronization of coupled neural networks with multiple switching topologies via adaptive control techniques

Abstract This research paper primarily focuses on the synchronization of a specific class of multi‐weighted coupled neural networks (MWCNNs) with switching topology, employing two adaptive control methods. In complex environments and under the influence of communication disturbances, the topology structures of coupled neural networks with multiple weights inevitably undergo time‐varying changes. To address this, we propose a novel type of MWCNNs with switching topologies. To ensure synchronization within this network, we develop sufficient conditions based on Lyapunov functional and inequality techniques. These conditions guarantee the achievement of synchronization. Moreover, we address the synchronization problem by employing node‐based and edge‐based adaptive controllers. Finally, we provide a numerical example to demonstrate the effectiveness of the obtained results. This example serves as empirical evidence showcasing the successful application of the proposed synchronization approach in practical scenarios.