Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9502668 | Journal of Mathematical Analysis and Applications | 2005 | 9 Pages |
Abstract
In this paper, we use a method different from the known literature to investigate the qualitative properties of the following fourth-order rational difference equation: xn+1=xnxnâ1xnâ3+xn+xnâ1+xnâ3+axnxnâ1+xnxnâ3+xnâ1xnâ3+1+a,n=0,1,2,â¦, where aâ[0,â) and the initial values xâ3,xâ2,xâ1,x0â(0,â). The successive lengths of positive and negative semicycles of nontrivial solutions of the above equation is found to periodically occur, that is, â¦,3+,2â,1+,1â,3+,2â,1+,1â,3+,2â,1+,1â,3+,2â,1+,1â,â¦, or, â¦,2+,1â,1+,3â,2+,1â,1+,3â,2+,1â,1+,3â,2+,1â,1+,3â,2+,1â,1+,3â,â¦. By using the rule, the positive equilibrium point of the equation is verified to be globally asymptotically stable.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xianyi Li,