On The Dynamical Behaviors In Nonautonomous Fuzzy Cellular Neural Networks With Time Varying

Since neural networks have enormous potential in wide varieties of appli-cations, many specialists and scholars apply themselves to the research of thetheory and achieve many perfect productions. In this paper, we perform re-searches of the stability and existence of periodic solution of fuzzy cellular neuralnetworks (FCNNs). The main contents of this paper include: the existence ofperiodic solution and the stability analysis for a class of FCNNs with variable co-e?cients and time-varying delays,and boundedness and exponential stability fornonautonomous FCNNs with reaction-di?usion terms and time-varying delaysrespectively.The main contents in this paper can be summarized as follows:1. Firstly, in the first section of the first chapter, we introduce the develop-mental process and significance of neural networks. In the following section 2 weintroduce the models of cellular neural networks. In section 3, we introduce theresearch results for fuzzy cellular neural networks. In section 4, the organizationof this paper is given.2. In the second chapter, we investigate the fuzzy cellular neural networks(FCNNs) with variable coe?cients and time-varying delays. A series of simplesu?cient conditions is obtained for checking the boundedness, global exponentialstability and the existence and global exponential stability of periodic solutionsof FCNNs with variable coe?cients and time-varying delays by using Younginequality and general Lyapunov functional.3. In the third chapter, a class of fuzzy cellular neural networks (FCNNs)with distributed delays and variable coe?cients is discussed. By applying the matrix theory and the inequality analysis technique, some su?cient conditions onthe existence, global exponential stability and weak global exponential stabilityof periodic solutions are established. Particularly, di?erently from some previousworks, in this paper, we do not require the coe?cients ci(t)(i = 1,2,···,n) inthe system are positive.4. In the forth chapter, nonautonomous fuzzy cellular neural networks withreaction-di?usion terms and time-varying delays are studied. By applying theinequality analysis technique, introducing ingeniously many real parameters andconstructing new auxiliary functions, some new and useful criteria on the bound-edness and global exponential stability are established. Finally, we give twoexamples to illustrate the e?ciency of our results.