Dynamic Analysis And Synchronization Control Of Memristor-based Recurrent Neural Networks With Time Delays

The researches about memristor and memristor-based nonlinear systems have devel-oped rapidly since the invention of a TiO2-based practical memristor device by scientists of Hewlett-Packard Laboratory in2008. The memristor-based neural network systems which are established from the circuit (VLSI Circuits) systems becoming the focus of research. The studies of memristor-based neural network systems can help to understand the behav-ior of many nonlinear systems, such as physical and biological systems. Memristor-based neural systems are presenting tremendous potential because of memristor has the follow-ing features:memory characteristics, nano size, low power consumption and fast switch-ing. 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 memristor-based 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 right-hand side. However, memristor-based neural networks are the dy-namic systems with discontinuous right-hand side. So, the classical research methods for the dynamical behaviors of differential equations with continuous right-hand side can not apply here. To solve this problem, here we employ the theories of differential inclusions and set-valued maps to deal with the switching terms, and this method is very effective to discuss the dynamical behaviors of memristor-based neural networks. At the same time, be-cause the memristor-based neural networks are switching systems with coefficients depends on the state, so the research methods and results of neural networks with discontinuous ac-tivation function can also not be directly applied to the memristor-based 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 re-sults obtained here are different from the researches only consider monotone nondecreasing feedback functions. Comparing with the researches on stabilization and synchronization of delayed memristor-based recurrent neural networks basing on2-norm, our researches are based on the p-norm. Intermittent control is the first time to introduce to study stabilization and synchronization of delayed memristor-based recurrent neural networks.This paper mainly studies the stability, periodic stability, exponential stabilization, syn-chronization control of memristor-based neurodynamic systems. By using the theory and techniques such as:the theory of dynamic system with discontinuous right-hand side, Lya- punov functional and inequalities technique, some algebraic criteria are given to show the dynamic evolution mechanism of delayed memristor-based recurrent neural networks. The main contents of this dissertation are listed as follows:A class of memristor-based recurrent neural networks with time delays and zero exter-nal input is studied. By using the mean value inequality, Cauchy-Schwarz inequality and the proper Lyapunov function, some algebraic criteria on global stability of memristor-based recurrent neural networks with times delays are obtained basing on2-norm. These results can characterize the fundamental stable properties of memristor devices, and provide con-venience for its practical applications. Numerical simulations illustrate the validity of the results and the effectiveness of the research methods.For the memristor-based delayed recurrent neural networks with zero external input, intermittent feedback controller is designed. By constructing appropriate Lyapunov func-tional, some algebra criteria on exponential stabilization are obtained basing on p(p≥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 memristor-based 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 memristor-based recurrent neural networks with time delays and periodic external input are established basing on p(p≥2)-norm. These criteria are deeply reveal the periodic dynamical mechanism of the memristor-based recurrent neural networks with time delays and periodic external input.A class of memristor-based delayed recurrent neural networks with constant external input is discussed. By constructing appropriate Lyapunov functional, basing on p(p≥2)-norm, some algebra criteria on exponential synchronization are established via continuous feedback control. These criteria are reveal the synchronization dynamical mechanism of the memristor-based delayed recurrent neural networks with constant external input. Because of the memristor-based delayed recurrent neural networks with discontinuous right-hand 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 memristor-based delayed recurrent neural networks. By constructing appropriate Lyapunov functional and basing on p(p≥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 memristor-based delayed recurrent neural networks basing on2-norm, the results obtained here are more general. And these criteria contain more variables, which have more flexibility and superiority.