Qualitaticce Study Of Bidirectional Associative Memory Neural Networks With Delays

Using the coincidence degree theory, exponential dichotomy theory and the Lyapunov functional method, we discuss the global exponential stability as well as the existence of periodic solution and almost periodic solution to the delayed bidirectional associative memory neural networks, and we obtain a series of new results. Many related results reported in the literature are extended or improved.In chapter 1, we state the background of the bidirectional associative memory neural networks and the theorial and practical significance of main works.In chapter 2, we dicuss the global exponential stability of equlibrium point for bidirectional associative memory neural networks, by only using some analytic techniques. Exponential converging velocity indexes are obtained, which depend on the delays and system parameters. We throw off the usual assumption that, the activation function is of bounded character. These results can apply to many activative functions, including the usual sigmoid functions and piecewise linear functions. New results are less conservative as compared to those reported in the previous literature. Especialy, we provide a method by solving algebra equations to obtain exponential converging velocity index, which depend on the delays and system parameters. These results indicate explicitly the effect of time delays on exponential convergence velocity index of the neural networks. These possess an important leading significance in the design and applications of globally exponentially stable bidirectional associative memory with transmission delays.In chapter 3, using the continuation theorem of Mawhin's coincidence degree theory, the Lyapunov functional method and the Yang's inequality technique, new sufficient conditions are obtained to ensure the existence and global exponential stability of periodic solution to the bidirectional associative memory neural networks with periodic coefficients and delays, which also throw off the usual assumption that the activation function is of bounded character.In chapter 4, we consider the neural networks which usually have a spatial extent due to the presence of an amount of parallel pathways with a variety of axon sizes and lengths. The transmission of signals is no longer instantaneous , there will be a distribution of transmission delays. The neural networks model with distributed time delays takes into account precisely for the spatial effects through the...