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Báo cáo hóa học: "ON THE SYSTEM OF RATIONAL DIFFERENCE EQUATIONS xn+1 = f (yn−q ,xn−s ), yn+1 = g(xn−t , yn− p )"

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: ON THE SYSTEM OF RATIONAL DIFFERENCE EQUATIONS xn+1 = f (yn−q ,xn−s ), yn+1 = g(xn−t , yn− p ) | ON THE SYSTEM OF RATIONAL DIFFERENCE EQUATIONS Xn 1 f yn-q xn-s yn 1 g xn-t yn-p TAIXIANG SUN AND HONGJIAN XI Received 20 March 2006 Revised 19 May 2006 Accepted 28 May 2006 We study the global behavior of positive solutions of the system of rational difference equations Xn 1 f yn-q Xn-s yn 1 g xn-t yn-p n 0 1 2 . where p q s t e 0 1 2 . with s t and p q the initial values x-s x-s 1 . x0 y-p y-p 1 . y0 e 0 to . We give sufficient conditions under which every positive solution of this system converges to the unique positive equilibrium. Copyright 2006 T. Sun and H. Xi. 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 In this paper we study the convergence of positive solutions of a system of rational difference equations. Recently there has been published quite a lot of works concerning the behavior of positive solutions of systems of rational difference equations 1-7 9 11 . Not only these results are valuable in their own right but also they can provide insight into their differential counterparts. Papaschinopoulos and Schinas 10 studied the oscillatory behavior the periodicity and the asymptotic behavior of the positive solutions of systems of rational difference equations Xn 1 A n yn 1 A n n 0 1 . 1.1 yn Xn where A e 0 ro and the initial values x-1 x0 y-1 y0 e 0 to . Recently Kulenovic and Nurkanovic 8 investigated the global asymptotic behavior of solutions of systems of rational difference equations a xn d yn Xn 1 K . . yn 1 n 0 1 . b yn e Xn 1.2 where a b d e e 0 ro and the initial values x0 y0 e 0 to . Hindawi Publishing Corporation Advances in Difference Equations Volume 2006 Article ID 51520 Pages 1-8 DOI 10.1155 ADE 2006 51520 2 The system of difference equations In this paper we consider the more general equation xn 1 f yn-q xn-s yn 1 g xn-t yn-p 1.3 where p q s t e 0 1 2 . with s