The Studies On Dynamical Behavior Of BAM Neural Networks And Competitive Neural Networks

As a result of the broad spectrum of applications in optimization,signal processing,image processing,pattern recognition and associativememory and so on, the artificial neural network has been fully developed.Artificial neural network information processing capacity depends on itsdynamical characteristics. Therefore, the study of artificial neuralnetwork dynamical features such as stability, peiodicity and other issues,has become an indispensable prerequisite in the artificial neural networkdesign.BAM neural network and competitive neural network are two classesof widely used neural networks.While running in a neural network,thesystem appears inevitable time delays,so the study of neural networkswith time delays is more practical significance.From the point of view about biological neural network systems,thehuman brain often changes in the regular periodic or chaotic state,so thecycle of neural networks and chaotic phenomena consussion study has morepractical significance.In fact,almost period contains period.Inaddition,the convergence rate of the equilibrium point of neural networksis an important indicator which is a measure of networks’performance.Inorder to reduce the required computation time of neural networks,in thedesign of neural networks,usually require the equilibrium point which hasthe exponential convergence.This paper has done the following work:1. The background and preliminary knowledge of neural networks areintroduced.2. The global asympotic stability of almost periodic solution for BAMneural networks with continuously distributed delays are established inBanach space by using the fixed point theorem, exponential dichotomy andconstructing Lyapunov function. An example is given to evaluate theavailability of the proceeding result.3.The global expoential stability of a kind of competitive Neuralnetworks with S-type distributed delays is studied by using the M-matrixtheory,homeorphism and Lyapunov function.4. Invariant set and attract set of the competitive neural networks withS-type distributed delays are derived by using nonnegative matrices anddifferential inequalities technique.