The researches about memristor and memristorbased nonlinear systems have developed rapidly since the invention of a TiO2based practical memristor device by scientists of HewlettPackard Laboratory in2008. The memristorbased neural network systems which are established from the circuit (VLSI Circuits) systems becoming the focus of research. The studies of memristorbased neural network systems can help to understand the behavior of many nonlinear systems, such as physical and biological systems. Memristorbased neural systems are presenting tremendous potential because of memristor has the following features:memory characteristics, nano size, low power consumption and fast switching. Generally speaking, the previous development of theory is the basis of the research and development of technology, therefore, theoretical research on the dynamic behaviors of memristorbased neural systems pave the way for it applied to various fields.At present, there are a lot of results on the dynamical behaviors of neural networks with continuous righthand side. However, memristorbased neural networks are the dynamic systems with discontinuous righthand side. So, the classical research methods for the dynamical behaviors of differential equations with continuous righthand side can not apply here. To solve this problem, here we employ the theories of differential inclusions and setvalued maps to deal with the switching terms, and this method is very effective to discuss the dynamical behaviors of memristorbased neural networks. At the same time, because the memristorbased neural networks are switching systems with coefficients depends on the state, so the research methods and results of neural networks with discontinuous activation function can also not be directly applied to the memristorbased neural networks, therefore some new research methods are developed here to deal with the difficulty. And the neural feedback functions not only cover the bounded functions, monotone nondecreasing functions, but also cover functions which satisfy the Lipschitz condition, therefore, the results obtained here are different from the researches only consider monotone nondecreasing feedback functions. Comparing with the researches on stabilization and synchronization of delayed memristorbased recurrent neural networks basing on2norm, our researches are based on the pnorm. Intermittent control is the first time to introduce to study stabilization and synchronization of delayed memristorbased recurrent neural networks.This paper mainly studies the stability, periodic stability, exponential stabilization, synchronization control of memristorbased neurodynamic systems. By using the theory and techniques such as:the theory of dynamic system with discontinuous righthand side, Lya punov functional and inequalities technique, some algebraic criteria are given to show the dynamic evolution mechanism of delayed memristorbased recurrent neural networks. The main contents of this dissertation are listed as follows:A class of memristorbased recurrent neural networks with time delays and zero external input is studied. By using the mean value inequality, CauchySchwarz inequality and the proper Lyapunov function, some algebraic criteria on global stability of memristorbased recurrent neural networks with times delays are obtained basing on2norm. These results can characterize the fundamental stable properties of memristor devices, and provide convenience for its practical applications. Numerical simulations illustrate the validity of the results and the effectiveness of the research methods.For the memristorbased delayed recurrent neural networks with zero external input, intermittent feedback controller is designed. By constructing appropriate Lyapunov functional, some algebra criteria on exponential stabilization are obtained basing on p(pâ‰¥1)norm. These criteria can be easily verified, and the neural feedback functions not only cover the bounded functions, monotone nondecreasing functions, but also cover functions which satisfy the Lipschitz condition, therefore, the results obtained here are more general and they also extend some existing results. Numerical simulations demonstrate the validity and superiority of the obtained results.Global periodic stability for a class of memristorbased recurrent neural networks with time delays and periodic external input is investigated. Under the framework of Filippov solution, the existing of periodic solution is given basing on the theory of fixed point. By constructing appropriate Lyapunov functional and using Young inequality, some algebraic criteria on global periodic stability of a class of memristorbased recurrent neural networks with time delays and periodic external input are established basing on p(pâ‰¥2)norm. These criteria are deeply reveal the periodic dynamical mechanism of the memristorbased recurrent neural networks with time delays and periodic external input.A class of memristorbased delayed recurrent neural networks with constant external input is discussed. By constructing appropriate Lyapunov functional, basing on p(pâ‰¥2)norm, some algebra criteria on exponential synchronization are established via continuous feedback control. These criteria are reveal the synchronization dynamical mechanism of the memristorbased delayed recurrent neural networks with constant external input. Because of the memristorbased delayed recurrent neural networks with discontinuous righthand side, which can exhibit more complex chaotic dynamics behavior, its signals are more difficult to be captured. Therefore, the analytical results can be applied to secure communication and more safe during the information transmission.This paper analyzes a class of memristorbased delayed recurrent neural networks. By constructing appropriate Lyapunov functional and basing on p(pâ‰¥1)norm, some algebra criteria on exponential synchronization are achieved via intermittent feedback control. Comparing with continuous feedback control, intermittent control is more economic. Different from the results on exponential synchronization of memristorbased delayed recurrent neural networks basing on2norm, the results obtained here are more general. And these criteria contain more variables, which have more flexibility and superiority.
