Study Of Dynamic Performance Of The Memristor-based Neural Networks

Memristor-based neural networks is a very important branch of neural networks. It has a variety of dynamic performance. And it has important applications in image denoising, pattern recognition,associative memory and secure communication. The research of dynamic performance of the memristor-based neural networks is not only of theoretical significance, but also the theory of memristor-based neural networks ia applied in applications, so it has practical significance.Based on Lyapunov stability theory, combining with M-matrix, by using homeomorphism mapping, the differential equation with a discontinuous right-hand side theory,Halanay inequality, differential inclusion, drive-response concept as the main techniques,and may further research the memristor-based neural networks. The main contributions can be generalized as follows:1. Problems for global exponential stability of memristor-based recurrent neural networks with time delay are studied. By employing homeomorphism mapping, Lyapunov functionals and differential theory, the existence and uniqueness of the equilibrium point of memristor-based neural networks are proved and the equilibrium is global asymptotic stability,some M-matrix based conditions are obtained. In addition, the conditions improve some previous criteria based on M-matrix and have robustness for different time delays and activation functions. Besides, the conditions are easy to be verified with the physical parameters of system itself.2. Schemes for global exponential periodicity problem about a general memristorbased recurrent neural networks with time-varying delays are discussed. Via two proper Lyapunov functional, the Halanay inequality and the theory of differential equations with discontinuous right-hand sides, the symmetry and asymmetric connection weights are considered in the switching state, some new conditions concerning global exponential periodicity are obtained. Simulation confirmed the effectiveness and feasibility of the proposed methods.3. On the basis of event-driven control synchronization of memristor-based competitive neural networks with different time scales is developed. By constructing a proper Lyapunov functional, as well as employing differential inclusion theory, a delay-independent controller is designed to achieve the asymptotic synchronization of coupled competitive neural networks. Chaotic synchronization of memristor-based neural networks with different time scales is applied to secure communication. The transmitted signal can be superimposed with the chaotic signal, and the original signal can complete reproduction at receiving end. A simulation example is given to show the effectiveness of the secure communication.