Dynamical Properties for a Class of Fourth-Order Nonlinear Difference Equations

被引：0
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作者：
Dongsheng Li
Pingping Li
Xianyi Li
机构：
[1] Jiangsu University,Ministry Education Key Laboratory of Modern Agricultural Equipment and Technology
[2] University of South China,School of Economics and Management
[3] Shenzhen University,College of Mathematics and Computational Science
来源：
Advances in Difference Equations | / 2008卷
关键词：
Difference Equation; Asymptotic Stability; Cycle Length; Nontrivial Solution; Global Attractor;
D O I：
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摘要：
We consider the dynamical properties for a kind of fourth-order rational difference equations. The key is for us to find that the successive lengths of positive and negative semicycles for nontrivial solutions of this equation periodically occur with same prime period 5. Although the period is same, the order for the successive lengths of positive and negative semicycles is completely different. The rule is [inline-graphic not available: see fulltext] or [inline-graphic not available: see fulltext] or [inline-graphic not available: see fulltext]. By the use of the rule, the positive equilibrium point of this equation is proved to be globally asymptotically stable.
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