Existence And Uniqueness Of Equilibrium, Periodic Solution, Almost Periodic Solution And Global Exponential Stability For Neural Networks With Time-varying Delays

In this paper, based on the method of variable replacement, real parameters di > 0 (i = 1,2, ... , n) which can be adjusted, are introduced ingeniously. We establish some new sufficient conditions for the existence, uniqueness and global exponential stability of the equilibrium, periodic solution and almost periodic solution of neural networks with time-varying delays by means of the method of variation of parameters, fixed point theorem and some analysis techniques. Our results generalize and improve the related results in [21-25]. By our results, we can judge some problems that can not be judged in literature [26]. These conditions can be used both to design globally exponentially stable and periodical oscillatory neural networks with time-varying delays, and to enlarge the area of designing neural networks. Our work has important significance in related theory and it's application.The thesis is divided into 6 sections. In section 1, introduction is given. It covers the models of neural networks which many reseachers studied in recent years, and the model of neural networks which is studied in this paper. In section 2, some preliminaries, lemmas and base knowledge are mentioned. In section 3,4,5, we respectively prove the existence and uniqueness of equilibrium, periodic solution and almost periodic solution and the global exponential stability. In section 6, some applied examples are given.