Exponential Stability Analysis For Two Classes Of Static Recurrent Neural Networks With Delays

Recurrent neural network as a kind of nonlinear information processingsystem, has been applied in the field of associative memory, optimizationproblem, signal processing, pattern recognition and so on, because the dynamicbehavior of the neural network decided their processing functions. Therefore, itis important to study the dynamic behaviors of recurrent neural network forpractical applications. On the basis of different variable, recurrent neural networkcan be divided into local recurrent neural network and static recurrent neuralnetwork. Now, the local recurrent neural network has been studied extensively.However, a few works about static recurrent neural network have beenpublished. Based on its strong application background, this paper discusses thestability for two kinds of static recurrent neural networks.This paper is divided into four chapters:In chapter1, the development of neural network, current situations, mainworks, some definitions and theorems have been introduced.In chapter2, the robust exponential stability for a class of static recurrentneural network with S-type distributed delays on infinite interval has beendiscussed. By using homeomorphism mapping and generalized Halanayinequality approach, we have studied the existence, uniqueness and globalexponential stability of the equilibrium. The results of related references areextended.In chapter3, the almost periodic solution for a class of static recurrentneural network with S-type distributed delays on infinite interval has beendiscussed. By using Banach fixed point theory and Lyapunov functional method, we have studied the existence, uniqueness and global exponential stability of thealmost periodic solution.In chapter4discusses the P-order uniform boundedness, P-orderuniformly ultimate boundedness and P-order global exponential stability for aclass of static recurrent neural network with reaction-diffusion and time-varyingdelays have been discussed by using Lyapunov functional and inequalitytechnique.