作者机构：
[Liao, Xinyuan] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;Shanghai Univ, Dept Mat Sci, Shanghai 200444, Peoples R China.;Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China.
通讯机构：
[Liao, Xinyuan] N;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
作者机构：
[熊岳山] College of Sciences, National Univ. of Defense Technology, Changsha 410073, China;School of Mathematics and Physics, Nanhua University, Hengyang 421001, China;Changsha University, Changsha 410003, China;[蔡放] College of Sciences, National Univ. of Defense Technology, Changsha 410073, China, Changsha University, Changsha 410003, China;[王礼广] College of Sciences, National Univ. of Defense Technology, Changsha 410073, China, School of Mathematics and Physics, Nanhua University, Hengyang 421001, China
通讯机构：
[Wang, L.-G.] C;College of Sciences, National Univ. of Defense Technology, China
期刊：
Indian Journal of Pure and Applied Mathematics,2007年38(6):579-587 ISSN：0019-5588
通讯作者：
Li, Xianyi
作者机构：
[Li, Xianyi; Li, XY] Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Li, Xianyi] N;Nanhua Univ, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Global asymptotic stability;Length of semicycle;Periodicity;Perturbation;Rational difference equation;Semicycle;Trajectory structure rule
摘要：
In this paper the following fourth-order rational difference equation Xn+1 = Xnxn-2b + x n-3b + a / xn-2b + x nxn-3b + a, n = 0, 1, 2, . . ., where a, b ε [0, ∞) and the initial values x-3, x-2, x-1, x0 ε (0, ∞), is considered. It is found that the perturbation of the initial values may lead to the variation of the trajectory structure rule for the solutions of the above equation. That is, with the change of the initial values, the successive lengths of positive and negative semicycles for nontrivial solutions of this equation is found to periodically occur with prime period 15, i.e., . . . 4+, 1 -, 1+, 1-, 2+, 2-, 1 +, 3-, 4+, 1-, l+, 1 -, 2+, 2-, 1+, 3-, 4 +, 1-, l+, 1-, 2+, 2 -, 1+, 3-, . . . . By the use of the rule, the positive equilibrium point of the equation is verified to be globally asymptotically stable.
作者机构：
[王智慧] Department of Mathematics, Shaoyang University, Shaoyang 422004, China;[欧阳自根] Department of Mathematics, Nanhua University, Hengyang 421001, China;[罗李平] Department of Mathematics, Hengyang Normal University, Hengyang 421008, China
期刊：
Applied Mathematics and Computation,2006年181(2):803-815 ISSN：0096-3003
通讯作者：
Chen, FD
作者机构：
[Chen, Fengde] College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350002, China;[Huang, Zhenkun] School of Sciences, Jimei University, Xiamen, Fujian 361021, China;[Liao, Xinyuan] Department of Mathematics, Shanghai University, Shanghai, 200444, China;[Liao, Xinyuan] School of Mathematics and Physics, Nanhua University, Hengyang, Hunan 421001, China
通讯机构：
[Chen, FD ] ;Fuzhou Univ, Coll Math & Comp Sci, Fujian 350002, Peoples R China.
摘要：
In this paper, the basic definitions of inner-product and outer-product of Vague set are introduced. Based on that, some characters of them are brought forward and the particular proof are presented afterward.
