Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4626850 | Applied Mathematics and Computation | 2015 | 8 Pages |
Abstract
We study the global asymptotic stability of solutions of the following two difference equationsxn+2xn=a+bxn+1+(1-c)xn+12+cxn2,n=0,1,2,…andxn+2xn=a+bxn+1+d(1-c)xn+12d+xn+1+cxn2,n=0,1,2,…,where a∈(0,+∞),d∈[0,+∞),c∈(0,1]a∈(0,+∞),d∈[0,+∞),c∈(0,1] and the initial values x0,x1∈(0,+∞)x0,x1∈(0,+∞). Bastien and Rogalski (2004) showed if c=0c=0 then there exist all the possible periods for the solutions of the above equations. Using an extension of the quasi-Lyapunov method, we prove that the sequences generated by the first difference equation are globally asymptotically stable where 0
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Guifeng Deng, Fengjie Geng, Yun Zhang,