Study Of Periodic And Almost Periodic Solution For Neural Networks With Time Delays

In the recent decade, more and more scientific scholars are interesting in the theory and application of artificial neural networks, which is one of the most active research in the area of the nonlinear science. The main reasons are that artificial neural networks have plenty of dynamical behaviors such as stability, oscillation and chaos. From the investigations of the biological neural networks, it is known that human's brain is in periodic oscillatory or chaos all the time. So it is very important and useful to investigate periodic oscillatory and chaos of the artificial neural networks. Many results have been obtained in the field of periodic oscillatory or chaos of the cellular neural networks(CNN), Hopfield neural networks and bidirectional associative memory neural networks(BAM). Competitive neural networks with different time-scales and static neural network models are proposed recently. Few paper studies the dynamical behaviors of the two models, especially their periodic and almost periodic solutions. This paper investigates the periodic solution of the static neural networks with delays and almost periodic solution of the competitive neural networks with time delays and different time-scales. The main results of the paper are as followsIn chapter 1, the general knowledge of neural networks is introduced, and the preliminary knowledge which is used in the thesis is given..In chapter 2, the almost periodic solution for competitive neural networks with time delays and different time-scales is investigated by using the fixed point theory, properties of matrix and the Lyapunov function. The method used in the proof is different with reference [11]. Sufficient conditions are established for the existence ,uniqueness and global exponential stability of it. MIn chapter 3, the almost periodic solution for competitive neural networks with distributed delays and different time-scales is studied by using the fixed point theory, properties of matrix and Lyapunov function. Sufficient conditions are established for the existence, uniqueness and global exponential stability of itMIn chapter 4, the existence and global robust exponential stability of periodic solution for the static neural network with time-delays is studied by using the fixed point theory , Poincare mapping, Lyapunov function and differential inequality technique.Some sufficient conditions are established for it.