期刊论文

Li, XY

英文

Computers & Mathematics with Applications

0898-1221

2005

49

5-6

723-730

10.1016/j.camwa.2004.10.033

The study of rational difference equations of order greater than one is quite challenging and rewarding because some prototypes for the development of the basic theory of the global behavior of nonlinear difference equations of order greater than one come from the results for rational difference equations. For this, see, for example, the papers in the journal of "Advances in Difference Equations" and the references cited therein. Furthermore, there have not been any effective This work is supported by NNSF of China (Grant: 10371040), Mathematical Tianyuan Foundation of China (Grant: TY10026002-01-05-03), Excellent Youth Item of EducationM Committee of Hunan Province (Grant: 04B056), Scientific Research Foundation of Educational Committee of Hunan Province (Grant: 99C146, 02C373) and Foundation for Youth Key Teachers of Hunan Province.

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In this paper, the rule for the lengths of positive and negative semicycles of nontrivial solutions of the following fourth-order rational difference equation,xn+1=xnbxn-2+xn-3b+axnb+xn-2xn-3b+a,n=0,1,2,..., where a, b ε [0, ∞) and the initial values x-3,x-2,x -1,x0 ε (0, ∞), to successively occur is found to be ..., 4+, 3-, 1+, 2-, 2 +, 1-, 1+, 1-, 4+, 3 -, 1+, 2-, 2+, 1-, 1 +, 1-, 4+, 3-, 1+, 2 -, 2+, 1-, 1+, 1-, ..., by which the positive equilibrium point of the equation is verified to be globally asympto...