The Global Dynamics Of Three Kinds Of Recurrent Neural Networks With S-Type Delays

The global asymptotical properties of three kinds of recurrent neural networks with S-type distributed delays were discussed in this paper.In the first chapter, the global exponential stability of the Cohen-Grossberg neural network with distributed delays was investigated. Bound of the system was solved by using Gronwall inequality, the existence and uniqueness of equilibrium was discussed by applying the theory of degree. Thereby a sufficient condition for the system to be global exponential stability is given by applying the Halanay inequality. At last an example was given, and the stimulation was presented.In the second chapter, the asymptotic behavior of the recurrent neural network with distributed delays was investigated, the dissipation of the system was solved by constructing a Lyapunov function with Razuminkhin condition, and the asymptotic compactness of the system was discussed by applying the technology of splitting the semigroup into two parts. Thereby a sufficient condition is given for the equation to have a global attractor by the existence theory of attractor.In the third chapter, the long time behavior of the solutions of a kind of Hopfield neural network with S-type distributed state-dependent delays and reaction-diffusion term was discussed. First of all, a generalization of the Halanay inequality was constructed, the existence of the solution of the system was solved by using the Faedo-Galerkin method, then, the uniqueness of the solution was treated by applying the Halanay inequality, and the dissipate of the system was obtained by applying the generalization of the Halanay inequality. The conditions for the existence of the global attractors were given at last.