Studies On Stability Of Neural Networks With Delays

In this dissertation, the existence and global exponential stability of equilibrium point and periodic solution are investigated deeply for some classes of artificial neural networks. The results are fairly new and helpful to design globally exponentially stable and oscillatory neural netwroks.Firstly, the existence and global stability of delayed fuzzy cellular neural networks (FCNN) with either constant delays or time-varying delays is proposed by using the theory of topological degree, Holdor inequality properties of nonsingular M-matrix and a suitable Lyapunov functional. The sufficient criteria are obtained for guaranteeing the global exponential stability of FCNN with constant and time-varying delays and the estimation of exponential convergence rate with regard to speed of vary of delays is presented.Secondly, some sufficient conditions that ensuring the global convergence and exponenetial convergence of a cellular neural netwoks with time-varying connection weights and time-varying delays are obtained by using a suitable Lyapunov functional, algebric inequality and improved Lyapunov theorem.Thirdly, by using integral inequality, the properties of nonsingular M-matrix and a continuation theorem based on coincidence degree, some new sufficint conditions are obtained ensuring existence of periodic solution of cellular neural networks with periodic coefficients and delays, and the global exponential stability of the periodic solution is studied by using variation of constant, integral inequality, Gronwall's Lemma, and at the same time, the exponentially convergent rates are also estimated.Fourthly, the existence and global exponential stability of periodic solution are discussed for the bidirectional associative memory (BAM) neural networks with periodic coefficients and delays. Some new sufficient conditions for ascertaining the existence and global exponential stability of the periodic solution of such BAM neural networks are obtained by using the properties of nonsingular M-matrix, integral inequality analysis and a continuation theorem based on coincidence degree. These conclusions are presented not only in terms of systems parameters but also the period of the system and the mean values of decaying rates.Finally, the global exponential stability of Cohen-Grossberg neural networks with time-varying delays is studied. By constructing several suitable Lyapunov functionals, some sufficient criteria for the global exponential stability and the exponential convergence rate of the equilibrium point of this system are obtained.