The Existence And The Stability Of Almost Periodic Solutions To Cohen-grossberg Neural Networks

In this paper, we mainly analysis the dynamic characteristics of the existence,uniqueness and the stability about almost periodic solutions to Cohen-Grossbergneural networks.The whole paper consists of the following chapters:In Chapter1, there are some backgrounds about the researches and developmentof neural networks and the progress about the existence, uniqueness and the stabilityof almost periodic solutions to Cohen-Grossberg neural networks.In Chapter2, the existence, uniqueness and the stability of almost periodicsolutions to a class of Cohen-Grossberg neural networks with distributed delays ontime scales is considered. In this chapter, without assuming bounded conditions onthese activation functions, we first use the inequality technique to ensure theexistence and uniqueness of the almost periodic solutions for Cohen-Grossbergneural networks on time scales. Next, by constructing the suitable Lyapunov function,we establish some sufficient conditions on global exponential stability of almostperiodic solutions. Because of the general of the activation function and thecharacteristics of the time scales, the results obtained in this chapter are generalizedcompared with the ones that obtained in published papers.In Chapter3, a class of stochastic Cohen-Grossberg neural networks (SCGNNS)with continuous distributed delays of neutral type is considered. In this chapter,firstly, some conditions are derived to ensure the existence and uniqueness of thealmost periodic solution by means of contraction mapping principle and inequalitytechniques. Then by employing the nonnegative semi-martingale convergencetheorem, the almost sure exponential stability of the SCGNNS is investigated, andsome new results are established. Finally, one example is given to illustrate theobtained results.In Chapter4, the global exponential stability in the mean square of stochasticCohen-Grossberg neural networks (SCGNNS) with mixed delays is studied. In thischapter, by applying the Lyapunov function, stochastic analysis technique andinequality techniques, some sufficient conditions are obtained to ensure theexponential stability in the mean square of the SCGNNS.In Chapter5, the automorphic solution, a generalized solution of almostperiodic solution, is considered. We first simplify the general CGNNS, and rewritten the model using the semi-discretization, In this chapter, By the contraction mappingprinciple, the existence and the uniqueness of almost automorphic solutions arediscussed, and some new results are obtained.After the analysis of different kinds of the existence and the stability for thealmost periodic solutions on CGNNS, the numerical simulation examples are givento illustrate the effectiveness and the feasibility of the theoretical results obtained.