Several Algebraic Conditions For Dynamics Of Memristor-based Neural Networks

For the sake of completeness of circuit theory, in 1971,the ethnic Chinese scientist-Chua firstly put forward the concept of memristor. As a new type of storage device, the memristor is bringing breakthroughs in many fields due to its various unique properties. In recent years, with the rapid development of artificial neural network, the study of the mechanism and application of the memristor-based neural network has became one of the hot spots and frontier problems in the subject.By using Lyapunov stability theory, the theory of set-valued mappings, linear ma-trix inequality, mathematical analysis techniques and combined with the characteristics of memristor, several kinds of memristor-based neural networks are studied and some preliminary theoretic principles on dynamic behaviors of these networks are obtained. The specific works of this dissertation are as follows:Chapter 1 gives the research background and significance of memristor-based neu-ral networks, including the introduction and development of memristor, the research status of memristor-based neural networks. Finally, some necessary preliminaries and the main contents of this dissertation are also introduced at the end of this chapter.Chapter 2 analyzes the impacts of time-varying delay on input-to-state stability of the memristor-based neural networks. Firstly, we establish the model of memristor-based neural networks with variable delays. In addition, by utilizing control theory and nonsmooth analysis, two new criteria and four corollaries ensuring the input-to-state stability are obtained. The conclusion herein contain some of the existing results.Chapter 3 discusses the model of memristor-based neural networks with interval discrete and distributed delays. By constructing proper Lyapunov functionals and some analysis techniques, we study the dissipativity of it. Finally, the delay-dependent and delay-independent dissipative conditions are derived, respectively.Chapter 4 studies the global exponential stability of stochastic memristor-based neural networks. On the one hand, we introduce the free-weighting parameters ki and other useful terms when estimating the upper bound of the Lyapunov function. On the other hand, we take the multi-terminal memristor state into account and utilize the intrinsic behaviors of memristor nonlinearity, which can be used to analyze the general stochastic memristor networks cluster. What is more, as far as i know, the related convergence rate has not been discussed in most of the articles regarding stochastic memristor-based systems, based on the conclusions of our paper, the convergence rate can easily be obtained through simple calculations.Finally, Chapter 5 summarizes the research conclusions and points out the prob-lems to be further research in the future.