Finite-Time Lag Synchronization of Memristive Neural Networks With Multi-Links via Adaptive Control

The finite-time lag synchronization problem of memristive neural networks with multi-links (MNNLs) is discussed with the adaptive controllers, and the discrete and distributed time-varying delays are included in the network models. With the Lyapunov functional method and the properties of inequality, two different finite-time methods are adopted to prove and compare the effects of the two proposed theorems, and three corollaries are obtained and to be analyzed. Using the assumptions of Lipschitz continuous and boundedness of the activation functions, three lemmas are derived to deal with the difficulty caused by the memristive jumping properties and synchronization lag feature, which make the proof of the theorems simple and clear. Based on that whether time-varying delays are included, with the adaptive control strategy, we design delay-independent and delay-dependent adaptive controllers with different adaptive parameters for the MNNLs respectively. Finally, two numerical simulations are given to show the effectiveness and correctness of the obtained theoretical results.