Adaptive Lag Synchronization of Memristive Neural Networks With Mixed Delays

This paper investigates the lag synchronization of memristive neural networks (MNNs) with mixed delays via adaptive control. Based on the switching jump properties of memristors and the assumption that the activation functions are bounded, three lemmas are derived first to deal with the theoretical analysis difficulties caused by the existences of time delays and time lag. By designing a series of suitable adaptive controllers, we prove that the considered MNNs can achieve asymptotic lag synchronization, exponential lag synchronization, and finite-time lag synchronization, respectively. Adaptive control can avoid the large control gains very well, and adaptive control can be used even when the system parameters are unknown. Moreover, extra calculations are not required to determine the appropriate control gains. Numerical simulations are presented to verify the effectiveness of the obtained theoretical results.