Almost Periodic Solution And Complete Periodic Synchronization Of Memristor-based Neural Networks With Time-varying Delays

Memristor has received a great deal of its potential application in next generationcomputer and powerful brain-like “neural” computer. Various memristor-based networkshave been established by means of the memristive circuits, and many applications havebeen made in science and engineering field. But very little attention has been paid todealing with the periodicity issue, in particular, to the best of our knowledge, the almostperiodic dynamics and the complete periodic synchronization of memristive neuralnetworks with time-varying delays has never been considered in the previous literature. Soin this paper, we emphasis these two issues.This paper is concerned with the dynamical stability analysis for almost periodicsolution of memristive meural networks with time-varying delays.On the one hand, with the frame of Filippov solutions, by applying the inequalityanalysis techniques, the existence and asymptotically almost periodic behavior ofsolutions are discussed. Based on the differential inclusions theory and Lyapunovfunctional approach, the stability issues of almost periodic solution is investigated, and asufficient condition for the existence, uniqueness and global exponential stability of thealmost periodic solution is established. Moreover, as a special case, the condition whichensures the global exponential stability of a unique periodic solution is also presented forthe memristive neural networks with time-varying delay. And, two examples are given toillustrate the corectness of the theoretical results about the almost periodic solution.On the other hand, this paper investigates the complete periodic synchronization ofmemristor-based neural networks with time-varying delays. First, with the frame ofFilippov solution, by using M-matrix theory and the Mawhin-like coincidence theorem inset-valued analysis, the existence of the periodic solution for the network system is proved.Second, complete periodic synchronization is considered for memristor-based neuralnetworks. According to the state-dependent switching feature of the memristor, the errorsystem is divided into four cases. Adaptive controller is designed such that the consideredmodel can realize global asymptotical synchronization. And an example is shown to demonstrate the corectness of the theoretical results about the complete periodicsynchronization.At last, we summarize the whole paper and the innovation points. And based on thearticles about memristor-based neural netwoks with time-varying delays we have now, wegive some outlook about distributed filtering, stochastic stabilization and robust faultdetection and so on, which haven’t been investigated but need to be.