Globally Asymptotical Stability Of High-order Delay Hopfield Neural Networks

This dissertation is composed of four chapters and mainly investigates four problems about the globally asymptotical stability(GAS) of the second-order delay Hopfield neural networks(HNN) with delay a constant. The four problems are of the following1. On the GAS of high-order delay HNN;2. On the parametric stability of high-order delay HNN;3. On the GAS of high-order delay HNN with time-varying coefficients;4. On the GAS of periodic solution of high-order delay HNN with periodic coefficients.In Chapter one, the history of the study about stability analysis of Hopfield neural networks is introduced accompanied with some prints of present work as well as the practical and theoretical values of this paper.In Chapter two, the problems 1-2 are investigated. By using the Brouwer fixed-point theorem, the equilibrium of the second-order delay Hopfield neural networks is proved exist. With the help of the equilibrium and the mean value of Lagrange theorem, the high-order delay model is changed into a lower one, then the sufficient conditions of GAS is given by using the classical Liapunov second method and LaSalle unvarying theorem. Meanwhile, from the GAS of the equilibrium, the uniqueness of the equilibrium is obtained. When the high-order delay model is changed into the lower one, some uncertain vector is produced, then parametric stability is considered for a special form of this model.In chapter three, the asymptotical stability of the second-order delay Hopfield neural networks with time-varying coefficients is considered. By using the similar argument presented in chapter one, the high-order delay model is changed into a lower one, then the sufficient conditions for asymptotical stability and globally asymptotical stability are given by using Liapunov functional and function.In chapter four, the existence of the periodic solution of high-order delay HNN with periodic coefficients is guaranteed by using the Fredholm operator and Mawhin's continuation theorem, then by using the Razumikhin-type theorem, the GAS of the equilibrium u;-periodic solution is obtained under some sufficient conditions.