Dynamical Behavior Of Hopfield Recurrent Neural Networks With S-type Distributed Delays

As a result of the broad spectrum of applications in optimization, signal processing, image processing, pattern recognition and associative memory and so on, the artificial neural network has been fully developed. Artificial neural network information processing capacity depends on its dynamic characteristics. Therefore, the study of artificial neural network dynamic features such as stability, periodicity and other issues, has become an indispensable prerequisite in the artificial neural network design. In particular, the local area recurrent neural network with the S-distribution delays include ones with discrete or distribution delays. Therefore, the study of dynamic features for the local area recurrent neural network with the S-distribution delays is more practical significance.From the point of view about biological neural network systems, the human brain often changes in the regular periodic or chaotic state, so the cycle of neural networks and chaotic phenomena concussion study has more practical significance. In fact, almost period contains period. In addition, running in a neural network, the system appears inevitable parameters fluctuation effect, which often leads to the design parameters of certain deviation from the value, in addition to the learning process, because of noise and some man-made mistakes inevitably distortion caused by the data will also affect the changes in synaptic strength. As the existence of parameter perturbations and outside interference, the study of neural network robust stability is very important.This paper includes four chapters:In chapter 1, the general knowledge of neural networks is introduced, and the preliminary knowledge which is used in the thesis is given.In chapter II, by using the fixed point theory and differential inequality technique we study the Existence and global attractivity of almost periodic solution for the local area recurrent neural network with the S-distribution delays. In chapter III, some sufficient conditions of existence for the invariant set and attract set of the local area recurrent neural network with the S-distribution delays are derived by using fixed point theory and differential inequality techniques.In chapter IV, global robust for stability of neural networks with S-type distributed delays has been discussed by employing topological degree theory homotopy invariance theory, functional inequality and Liapunov functional.