Cirtical Stability Analysis Of Delayed Static Neural Networks

Artificial neural network is a kind of nonlinear system which is used to process information.Artificial neural network is also known as recurrent neural network. It has been applied in all kind of fields like combinatorial optimization, pattern recognition, image processing, financial prediction, signal processing, automatic control, artificial intelligence.As a result,Artificial neural network has great potential and value.Upon the basis of different variable, artificial neural network can be divided into local recurrent neural network and static recurrent neural network. Few works about static recurrent neural network has been published up to now.And at present, most stability analysis of artificial neural network is not in critical conditions.Xu Zongben studied this kind of problem at first. A stability criterion about the neural network which activation function is sigmoid forms has been obtained.And the author studies the stability of static neural network with the nearest point projection mappings.Based on the previous literature,this paper discusses the exponential stability problem for a class of static neural network with projection mappings in critical condition.And the global attractivity of static neural networks with delays in critical condition.The main contents are shown as follows:1.The research background and significance, as well as the main research content of this paper are introduced.2.The critical exponential stability is discussed for static neural networks with the projection mappings,and a stability criterion is obtained by using the functional method. A few results of related literatures is extended.3.The existence of equilibrium point is discussed by using the topological degree theory,and the global attractiveness of static neural networks with delays in critical condition is studied by using the functional method.4.we discussed the global attractiveness of almost periodic solution of static neural networks with time-varying delays in critical condition,and a attractiveness criterion is obtained by using the Banach contract mapping theorem and functional method.