Analysis Of Different Types Of Hopfield Neural Networks

Neural network system is a complicated network system consisting of large numbers of simple neurons. Artificial neural network predigests, abstracts and simulates brain functions, is an abstract mathematical model. In recent years, academic researches for artificial neural network system played an important role in martial and civil fields and closely linked with capacity network design, fuzzy logic, numerical value computation and differential equation etc.Hopfield neural networks were first proposed by Hopfield in 1984. They have been widely studied both in theory and application. A lot of papers about Hopfield neural networks were published. Academicians are more interested in the networks with time-delay, which 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 problems.This dissertation mainly studies the stability of Hopfield neural networks and consists of five chapters. In chapter 1, the history of the study about Hopfield neural networks is introduced accompanied with some prints of present work as well as the practical and theoretical values of this dissertation. In chapter 2, the foundational knowledge about this dissertation is introduced. In chapter 3, a three-dimension discrete neural network model with multi-delays is obtained using Euler method. Furthermore, the linear stability of the model is studied using the discrete dynamic system theorem. Some conditions of ensuring the stability and the Hopf bifurcations are obtained. Finally, some numerical simulation supports our results. In chapter 4 and 5, Hopfield neural networks with piecewise constant argument are studied. Two simple and one three-neuron systems are established. Using the knowledge about EPCA and dynamical systems theory, we obtain some conditions of ensuring the stability and the Hopf bifurcations. Finally, some numerical simulation supports our results.