On The Dynamical Behaviors Of A Class Neural Networks With Time-varying

Since neural networks have enormous potential in wide varieties of applications, manyspecialists and scholars apply themselves to the research of the theory and achieve manyperfect productions. In this paper, we perform researches of dynamical behaviors ofthree classes of neural networks model with delays. The main contents of this paperinclude: the global exponential synchronization of fuzzy cellular neural networks withdelays and reaction-di?usion terms; the global exponential synchronization of impulsivefuzzy cellular neural networks with delays and reaction-di?usion term; the exponentialstability of multitime scale competitive neural networks with time-varying and distributeddelays.The main contents in this paper can be summarized as follows:The first section is introduction, firstly we introduce the developmental process andsignificance of neural networks. In the following section 2, we introduce the models ofneural networks and the research results for neural networks with delays. In section 3,the organization of this paper is given.In Section 2, the global exponential synchronization for a class of fuzzy cellular neu-ral networks with delays and reaction-di?usion terms is discussed. Some new su?cientconditions are obtained by using the Lyapunov functional method, many real parametersand inequality techniques. The result is also easy to check and plays an important role inthe design and application of globally exponentially synchronization. Finally, an exampleis given to verify our results.In Section 3, A class impulsive fuzzy cellular neural networks with delays and reaction-di?usion terms is discussed. Based on 2 norm, some new su?cient conditions are obtainedby using many real parameters and inequality techniques. The result is also easy tocheck and plays an important role in the design and application of globally exponentiallysynchronization. Finally, an example is given to verify our results. In Section 4, time-varying and distributed delays are introduced into competitiveneural networks and exponential stability for the neural network is investigated. Based onthe nonsmooth analysis techniques, we prove the existence and uniqueness of equilibriumfor system. By applying the matrix theory and the inequality techniques, exponentialstability of the equilibrium point are derived. Finally, an example is given to verify ourresults.