Passivity And Synchronization Problem Of Memristive Neural Networks

Imitations of the human central nervous system inspired the concept of neural networks. Most artificial neural networks are very effective at their intended tasks, though they bear only some resemblance to their more complex biological counterparts. Based on non-smooth analysis theory, this paper studies the passivity and synchronization of memristive neural networks. The main contributions of the dissertation are listed as follows:(1) The issue of exponential passivity of memristive neural networks with mixed time-varying delays is discussed. By constructing appropriate Lyapunov functionals and using new function technique, the exponential passivity criterion turns to four linear matrix inequalities that can be checked easily using an LMI toolbox. Non-positive definite matrices are used in Lyapunov functionals to make the results more reasonable.(2) Adaptive exponential synchronization for a general class of memristive neural networks with mixed time-varying delays is investigated. A new and simple adaptive controller with feedback control law is designed to achieve exponential synchronization by using Lyapunov functional method. The adaptive controller can be utilized for neural networks with different mathematical definitions of memristor. In addition, no excessive calculations such as solving linear matrix inequality or computing algebraic conditions are required in the synchronization criteria.(3) The problem of adaptive synchronization for memristive competitive neural networks with mixed time-varying delays and different time scales is studied. A simplification is conducted for the system to make it more suitable for mathematical operations. A simple, discontinuous and effective feedback adaptive controller is designed to ensure the synchronization. In the simulations, the conditons of the boundedness and global Lipschitz continuity of the activation function are analyzed by examples.