Periodic Solutions And Synchronization Problem Of Memristive Neural Networks

Neural network has been widely used in many fields, such as signal transmission,image processing, pattern recognition, automatic control, associative memory andcombinatorial optimization. What’s more, neural network has many good dynamicbehaviors, such as stability, chaos and synchronization, which are the prerequisite formany applications. Based on some modern mathematical theory such as differentialinclusion, nonsmooth analysis theory, Lyapunov method and by using linear matrixinequality (LMI) techniquenes, this paper mainly consentrate on the synchronizationcontrol of several types of memristive neural networks. The main results are listed asfollows:Firstly, a class of memristive neural networks with mixed time-varying delays isinvestigated, and the existence of the periodic solutions was given according to M matrix.Meanwhile, a proper adaptive controller was given to ensure the realization of anti-synchronization goal, what’s more, the designed controller depends on the swithing jumpof memristor;Secondly, the projective synchronization of a class of memistor-based neural networkswith time delays are discussed, by constrcting an appropriate adaptive controller, theweak, modified and functional projection synchronization of master-drive system wasachiebed;Finally, the finite-time synchronization of memristive neural networks with timedelays was studied. In order to make the master-slave system achieve finite-timesynchronization, an adaptive controller was designed. At the same time, the finite-timesynchronization criteria are given in terms of LMIs.