Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$
Abstract In this paper, we present the asymptotic behavior of the solutions for a general class of difference equations. We introduce general theorems in order to study the stability and periodicity of the solutions. Moreover, we use a new technique to study the existence of periodic solutions of th...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-12-01
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| Series: | Advances in Difference Equations |
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| Online Access: | http://link.springer.com/article/10.1186/s13662-018-1896-0 |
| _version_ | 1819268330039541760 |
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| author | Osama Moaaz |
| author_facet | Osama Moaaz |
| author_sort | Osama Moaaz |
| collection | DOAJ |
| description | Abstract In this paper, we present the asymptotic behavior of the solutions for a general class of difference equations. We introduce general theorems in order to study the stability and periodicity of the solutions. Moreover, we use a new technique to study the existence of periodic solutions of this general equation. By using our general results, we can study many special cases that have not been studied previously and some problems that were raised previously. Some numerical examples are provided to illustrate the new results. |
| first_indexed | 2024-12-23T21:31:20Z |
| format | Article |
| id | doaj.art-0106e536dbc04017859033434948b899 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-23T21:31:20Z |
| publishDate | 2018-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-0106e536dbc04017859033434948b8992022-12-21T17:30:27ZengSpringerOpenAdvances in Difference Equations1687-18472018-12-012018111410.1186/s13662-018-1896-0Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$Osama Moaaz0Department of Mathematics, Faculty of Science, Mansoura UniversityAbstract In this paper, we present the asymptotic behavior of the solutions for a general class of difference equations. We introduce general theorems in order to study the stability and periodicity of the solutions. Moreover, we use a new technique to study the existence of periodic solutions of this general equation. By using our general results, we can study many special cases that have not been studied previously and some problems that were raised previously. Some numerical examples are provided to illustrate the new results.http://link.springer.com/article/10.1186/s13662-018-1896-0Difference equationEquilibrium pointsLocal and global stabilityPrime period two |
| spellingShingle | Osama Moaaz Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$ Advances in Difference Equations Difference equation Equilibrium points Local and global stability Prime period two |
| title | Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$ |
| title_full | Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$ |
| title_fullStr | Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$ |
| title_full_unstemmed | Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$ |
| title_short | Dynamics of difference equation xn+1=f(xn−l,xn−k) $x_{n+1}=f( x_{n-l},x_{n-k})$ |
| title_sort | dynamics of difference equation xn 1 f xn l xn k x n 1 f x n l x n k |
| topic | Difference equation Equilibrium points Local and global stability Prime period two |
| url | http://link.springer.com/article/10.1186/s13662-018-1896-0 |
| work_keys_str_mv | AT osamamoaaz dynamicsofdifferenceequationxn1fxnlxnkxn1fxnlxnk |