Dynamic Behavior Of Delayed Artificial Neural Networks

In a definite delayed cellular neural network (DCNN) system, some important data are usually obtained by statistic method, such as the neuron charging time constants, the weights of the neuron interconnections and the delays in the process of the axonal signal transmission. Then, there must exist statistic errors. So it is necessary to study the DCNN system whose coefficients and parameters have their own rangeability. The attractors of dynamic system have attracted the interest of many researchers recently. Because the long-run dynamic behavior of dynamic system depends on the attractors, especially, a singular attractor has crucial function to the behavior of the system[25].In the first chapter of this thesis-Introduction, we introduce the development of delayed artificial neural networks.In the second chapter, we discuss the global robust stability of interval cellular neural networks with time-varying delays by the theory of topological degree and the method of Liapunov function. And a fairly general and convenient criterion is presented. The cellular neural network model considered in this paper includes many well-known neural network models as its special cases.In the third chapter, we analyze the global attractor of Hopfield reaction-diffusion neural networks with time-varying delays using the semigroup theory of operators, the inequality skills and the imbedding method in Sobolev space. A very useful and convenient criterion on the existence of the global attractor is given. Furthermore, we can estimate the location of this global attractor.