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: Qualitative behavior of a rational difference equation y = py++y yy | Qian and Qi-hong Advances in Difference Equations 2011 2011 6 http content 2011 1 6 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access yn yn-1 p ynyn-1 Qualitative behavior of a rational difference equation tn 1-Xiao Qian and Shi Qi-hong Correspondence xiaoxiao_xq168@ Department of Basic Courses Hebei Finance University Baoding 071000 China Abstract This article is concerned with the following rational difference equation yn 1 yn yn-1 p ynyn-1 with the initial conditions y-1 y0 are arbitrary positive real numbers and p is positive constant. Locally asymptotical stability and global attractivity of the equilibrium point of the equation are investigated and non-negative solution with prime period two cannot be found. Moreover simulation is shown to support the results. Keywords Global stability attractivity solution with prime period two numerical simulation Introduction Difference equations are applied in the field of biology engineer physics and so on 1 . The study of properties of rational difference equations has been an area of intense interest in the recent years 6 7 . There has been a lot of work deal with the qualitative behavior of rational difference equation. For example Qinar 2 has got the solutions of the following difference equation aXn-1 Xn 1 - . 1 bXnXn-1 Karatas et al. 3 gave that the solution of the difference equation xn- 5 Xn 1 1 xn- 2Xn-5 In this article we consider the qualitative behavior of rational difference equation yn yn-1 yn 1 - - 1 n -0 1 . 1 p ynyn-1 with initial conditions y-1 Jo e 0 p e R . Preliminaries and notation Let us introduce some basic definitions and some theorems that we need in what follows. Lemma 1. Let I be some interval of real numbers and f I2 I SpringerOpen0 2011 Qian and Qi-hong licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License http licenses by .
