Stability Analysis Of Neural Networks With Delays And Discrete-time Analogues

This dissertation presents some qualitative studies on dynamical behaviors of two kinds of neural networks models with delays which include globally asymptotic stability, the existence and exponential stability of almost periodic solutions, the existence and global attractivity of almost periodic sequence solutions.We generalize the content as following:(i) By constructing suitable Lyapunov functional, utilizing linear matrix inequality and matrix theory, we study delayed bidirectional associative memory neural networks. Some sufficient conditions, which are independent with the delayed quantity, are obtained for the global asymptotic stability. The sufficient criteria obtained are computationally more flexible and more efficient than many other existing criteria.(ii) By applying Banach fixed point theory, differential inequality techniques,we study Cohen-Grossberg neural networks with variable delays, and some sufficient conditions for the existence and exponential stability of almost periodic solutions for Cohen-Grossberg neural networks with variable delays are obtained. Some previous results are improved and extended.(iii) We investigate the discrete-time Cohen-Grossberg neural networks in the almost periodic case. Some suffcient conditions are obtained to guarantee the existence and global attractivity of almost periodic sequence solution of delayed discrete-time Cohen-Grossberg neural networks. It is believed that the conditions obtained will be useful for the design and applications of discrete-time Cohen-Grossberg neural networks with delays.