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The rule of semicycle and global asymptotic stability for a fourth-order rational difference equation

✍ Scribed by Xianyi Li; Deming Zhu

Publisher: Elsevier Science
Year: 2005
Tongue: English
Weight: 465 KB
Volume: 49
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2004.10.033

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✦ Synopsis

In this paper, the rule for the lengths of positive and negative semicycles of nontrivial solutions of the following fourth-order rational difference equation,

where a,b E [0, oo) and the initial values x-3,z-2, x-l,~c0 E (0, co), 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 asymptotically stable.

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