tailieunhanh - Báo cáo hóa học: "CONVERGENCE AND PERIODICITY OF SOLUTIONS FOR A CLASS OF DIFFERENCE SYSTEMS"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: CONVERGENCE AND PERIODICITY OF SOLUTIONS FOR A CLASS OF DIFFERENCE SYSTEMS | CONVERGENCE AND PERIODICITY OF SOLUTIONS FOR A CLASS OF DIFFERENCE SYSTEMS HONGHUA BIN LIHONG HUANG AND GUANG ZHANG Received 16 January 2006 Revised 27 July 2006 Accepted 28 July 2006 A class of difference systems of artificial neural network with two neurons is considered. Using iterative technique the sufficient conditions for convergence and periodicity of solutions are obtained in several cases. Copyright 2006 Honghua Bin et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction Consider the following difference system of the form Xn 1 Ảxn f yn n 0 1 2 . yn 1 Ayn f xn where A e 0 1 is a constant for any a b e R f R R is given by f u 1 0 u e a b u e a b . The system can be viewed as the discrete version of the following two-neuron network model dx -ax fy M dj -ay 0f x i where denotes the greatest integer function a 0 represents the internal decay rate Hindawi Publishing Corporation Advances in Difference Equations Volume 2006 Article ID 70461 Pages 1-10 DOI ADE 2006 70461 2 Convergence and periodicity ft 0 measures the synaptic strength x t and y t denote the activations of the corresponding neurons respectively and f is the activation function defined by . In recent years many research efforts have been made in neural modelling and analysis since one of the neural networks models with electronic circuit implementation was proposed by Hopfield in 6 . System describes the evolution of a network of two identical neurons with excitatory interactions which has found interesting applications in image processing of moving objects and has been investigated in 7 . In fact we can rewrite system as the following form d x t eat - fteatf y t d y t eat fteatf x t . Let n be a positive integer. We integrate from n to t e n n 1 and obtain x t eat - x n ean ft .