Stability Analysis Of Neural Networks Based On The Fixed Pointed Theorems

The theory and application of neural network model has become a hot topic in theinternational research in recent decades. As we know, neural network possesses goodapplication prospects in the areas of pattern recognition, signal and image process-ing, optimization problem and solving nonlinear algebraic equations. And this oftenrelies on dynamics analysis of neural network. Especially stability analysis of neuralnetworks can enlighten and guide practical application, so its strict analysis is veryimportant.In the frst chapter, we investigate the existence of periodic solution of im-pulsive bidrectional associative memory (BAM) networks on time scales. By using theLeray-Schauder fxed point theorem, we show that there exits a periodic solution ofBAM networks under bounded impulsive perturbation.In the second chapter, we dis-cuss Wilson-Cowan neural networks (WCNNs) with almost periodic coefcients. Byusing the fxed point theorem and Lyapunov functional technique, we obtain sufcientcondition guaranteeing that there exists an unique almost periodic solution of WCNNswhich is exponentially stable.In the third chapter, we consider Wilson-Cowan modelof neuronal population with time-varying delays. Some sufcient conditions for theexistence and delay-based exponential stability of a unique almost periodic solutionare established. The approaches are based on constructing Lyapunov functionals andthe well-known Banach contraction mapping principle.The innovation of this paper isanalysising the stability of BAM and Wilson-Cowan neural networks through the useof fxed point theorem. Some new results about the stability criteria are given. The re-sults are easily checkable. In particular, our results frst give almost periodic dynamicsanalysis for Wilson-Cowan neural networks.