Periodic Solutions,Almost Periodic Solutions And Global Exponential Stability For Cellular Neural Networks With Delays

In this thesis, we describe some important properties of the dynamic behaviors of several classes of delayed cellular neural networks models , which includes the existence , uniqeuness and exponential stability of the periodic solutions and the almost periodic solutions. It is consists of six chapters. As the introductions, in Chapter 1, the background and history of neural networks are briefly addressed, and the foundation that the neural networks are considered as dynamic models is expressed sketchly, and some notations and definitions are given in this chapter. In Chapter 2, by using the continuation theorem of coincidence degree theory, we will give some new sufficient conditions for the existence and uniqeuness of the periodic solutions to a class of neutral neural model of one neuron. The results of this chapter are new and they complement previously known results. In particular, they avoid the trantional assumptions in the in the literature. In Chapter 3, by using the continuation theorem of coincidence degree theory, we will give some new sufficient conditions for the existence of the periodic solutions to a class of neutral cellular neural networks models of two neurons. The results avoid the trantional Lipschitz conditions of signal transmission functions in the in the literature. In Chapter 4, cellular neural networks with time-varying delays and complex deviating arguments are considered. Sufficient conditions for the existence , uniqueness and exponential stability of the periodic solutions are established by using the continuation theorem of coincidence degree theory, nonnegative matrices theory and differential inequality technique. The results of this chapter are new and they complement previously known results. In Chapter 5 and In Chapter 6, cellular neural networks with constant delays and disdributed delays are considered. Sufficient conditions for the existence , uniqueness and exponential stability of the almost periodic solutions are established by using the fixed point theorem of Banach space, nonnegative matrices theory and differential inequality technique, which substantially extend and improve some important results in the literature.