Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions
For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn=anxn−1+bnf(xn−k), where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and sh...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2008/179589 |
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| Summary: | For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of the form xn=anxn−1+bnf(xn−k), where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illustrate our results. |
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| ISSN: | 1026-0226 1607-887X |