Stability Of Hopfield Neural Network With Distributed Delay

In this paper, stability of delayed Hopfield neural networks was studied. In chapter two, stability of Hopfield neural network with impulsive and time-varying delay was studied. By constructing Lyapunov function, using Razumikin technique and Hardy inequality, a sufficient criteria for existence and uniqueness to the equilibrium state was obtained and a sufficient condition of stability for the unique equilibrium was obtained. In chapter three, stability of stochastic Hopfield neural network with distributed delay was discussed. By using Lyapunov function and semimartingale convergence theorem, some sufficient conditions were obtained. One example was given to show the applicability of the proposed approach. In chapter four, stability of stochastic Hopfield neural networks model with diffusion and mixed delays was discussed. By constructing Lyapunov functional and using inequality, some delay-dependent stability conditions were obtained. An example was given to illustrate the applicability of the obtained result.