Stability Analysis Of Discrete Hopfield Neural Networks With Time-Delay

Neural networks is a kind of intelligent control technology, which can simulate human being's intelligent behavior, solve many complicated and nondeterministic nonlinear automation problems not settled by traditional automation technology. Therefore, during the last several decades the study of neuron network has aroused the general interest of academic field, with special attention given to Professor Hopfield of California Institute of Technology, who put forward successive neuron network model.The theory and application of the neural networks with time-delay is one of the international foreland problems at present. The time-delay not only has reflected the hardware reality such as limited switch speed of amplifier in the artificial neural networks, but also better simulates the time-delay character of biology neural networks. At the same time it is the need to solve certain actual problem.The Discrete Hopfield neural network(DHNN) is one of the famous neural networks with a wide range of applications, such as content addressable memory, pattern recognition, and combininatorial optimization. Such applications heavily depend on the dynamic behavior of the networks. Therefore the researches on the dynamic behavior are a necessary step for the design of the networks .The stability of DHNN not only is the foundation of the network's application, but also is the most basic and important problem. The researches on stability of the DHNN has attracted the considerable interest. DHNND is an extension of DHNN. Also, the stability of DHNND is an important problem.The paper gives a research on the stability of DHNN. It consists of five chapters. In chapter 1, some introductive materials are presented, including research background and significance of this dissertation with the history and current status, the main contents of the paper and the list of the results obtained by the author. In chapter 2, some simplification conditions are given on the stability of DHNN from mathematics angel. Also the global convergence condition is discussed. In chapter 3, the stability of DHNND is investigated, mainly including the stability of parallel, serial and general updating rule. For the fist time, the condition that the matrix need is weakened by the decomposition to the time delay matrix and introducing the parameter; When the threshold value is zero, the stability of DHNND is studied with the initial state X(0)≠X(1). The updating property of DHNND with general updating rule is given, which provides a certain theory to the optimized problem. This is the most important chapter in the paper. In chapter 4, the stability of DHNN is investigated by graph method. Furthermore, a special DHNND is analyzed. In chapter 5, the design of DHNN is given a thorough research.