Periodic Dynamics Behaves Of Some Recurrent Neural Networks With Delays

Due to the signal transmission, the opening and closing of switch need some time, the time-delay exists universally in the neural network, so when scholars study the neural network, they have established the model of the time-delay neural network.. Of which the delay recurrent neural network is a kind of important one, and it is also an important part of the delay dynamic system and possesses very abundant dynamics properties. Because of its important applications in artificial intelligence, signal processing, dynamic image processing and the optimization problems in overall situation,in recent years, the dynamics problems of the delay recurrent neural network have aroused wide attention and deep research in academic circles, emerging a series of profound results. This paper mainly focuses on a series of study on its stability and periodic solutions of the recurrent neural network and have achieved some profound results. These conclusions will provide the theory bases for the neural network which is designed with periodic solutions of the exponential stability in overall situation.The whole thesis is divided into six parts:In the first chapter, we firstly summarize the structure, function, characteristics and the development process of the neural network, and analyze the structure and dynamics features of the neural network, and then the paper has also made a general description of the recurrent neural network model which is studied, meanwhile, the main work and innovation of this thesis have been pointed out as well.In chapter 2, in order to facilitate our understanding, we summarized the competition and cooperation system, some basic definitions of the mixed monotone system and the results which are used in this article.In chapter 3, we study a kind of periodic solutions with autonomous 2-neurons Hopfield neural networks with distribute delays, first, we transform the system into three-dimensional constant autonomous system by means of a change, and then set up appropriate conditions to transform the system into the competition system, by using the results of competition system, we have proved the existence and stability of periodic solutions of the system.In the fourth chapter, we have studied a kind of the existence and exponential stability of periodic solution and anti-periodic solutions which transform connection weight into delay recurrent neural network, in general sense, by coupling, we established a new mixed monotone system, by using the basic theories of mixed monotone operator, we proved the boundness and convergence of the mixed monotone system solution, because of this, we can prove the existence of periodic solutions of the original system ,based on this, we have also given the existence of the anti-periodic solutions,exponential stability and a condition.In chapter 5, we have studied a kind of generally variable delay recurrent neural network model which has the existence and local exponential stability of multi-periodic solutions, by coupling, we established a new mixed monotone system, which possesses monotonous boundness and convergence in 2" separate areas, thus we get to the conclusion that 2" periodic solutions with local exponential stability exists in the original system.Chapter 6 gives a review of recent results on recurrent neural networks and the prospect of further research.