期刊论文

Li, Xianyi

英文

Applied Mathematics Letters

0893-9659

2006

19

11

1152-1158

10.1016/j.aml.2006.01.001

This work was supported by the NNSF of China (grant: 10371040), the Mathematical Tianyuan Foundation of China (grant: TY10026002-01-05-03), the Excellent Youth Project of the Educational Committee of Hunan Province (grant: 04B056), the Scientific Research Foundation of the Educational Committee of Hunan Province (grant: 99C146, 02C373), the Foundation for “Youth Key Teachers of Hunan Province”, the Foundation for “New Century Engineering of ‘121’ Talents in Hunan Province” and the Foundation for “Chief Professor of Mathematical Discipline in Hunan Province”.

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We consider in this work the fourth-order rational difference equation {Mathematical expression} where a ∈ [0, ∞) and the initial values x- 3, x- 2, x- 1, x0 ∈ (0, ∞). 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 change of the initial values, the successive lengths of positive and negative semicycles for nontrivial solutions of this equation are found to occur periodically, and furthermore the periodicity is completel...