Global attractivity of a higher order nonlinear difference equation with decreasing terms
In the present paper, we further study the asymptotical behavior of the following higher order nonlinear difference equation \begin{equation*} x(n+1)= ax(n)+ bf( x(n)) + cf(x(n-k)), \qquad n=0, 1, \dots \end{equation*} where $a, b $ and $c$ are constants with $0<a<1, 0\leq b<1, 0\leq c <...
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University of Szeged
2024-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10913 |
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| author | Xiao Wang Chuanxi Qian |
| author_facet | Xiao Wang Chuanxi Qian |
| author_sort | Xiao Wang |
| collection | DOAJ |
| description | In the present paper, we further study the asymptotical behavior of the following higher order nonlinear difference equation
\begin{equation*}
x(n+1)= ax(n)+ bf( x(n)) + cf(x(n-k)), \qquad n=0, 1, \dots
\end{equation*}
where $a, b $ and $c$ are constants with $0<a<1, 0\leq b<1, 0\leq c <1$ and $a+b+c=1$, $f\in C[[0, \infty), [0, \infty)] $ with $f(x)>0$ for $x>0$, and $k$ is a positive integer, which has been recently studied in: On global attractivity of a higher order difference equation and its applications [Electron. J. Qual. Theory Diff. Equ. 2022, No. 2, 1–14]. We obtain some new sufficient conditions for the global attractivity of positive solutions of the equation, and show the applications of these results to some population models. |
| format | Article |
| id | doaj-art-2019b816c5874111ba88cd7ef7a35f11 |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-2019b816c5874111ba88cd7ef7a35f112025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-03-0120241711510.14232/ejqtde.2024.1.1710913Global attractivity of a higher order nonlinear difference equation with decreasing termsXiao Wang0Chuanxi QianInstitute of Applied System Analysis, Jiangsu University, Zhenjiang, Jiangsu, P. R. ChinaIn the present paper, we further study the asymptotical behavior of the following higher order nonlinear difference equation \begin{equation*} x(n+1)= ax(n)+ bf( x(n)) + cf(x(n-k)), \qquad n=0, 1, \dots \end{equation*} where $a, b $ and $c$ are constants with $0<a<1, 0\leq b<1, 0\leq c <1$ and $a+b+c=1$, $f\in C[[0, \infty), [0, \infty)] $ with $f(x)>0$ for $x>0$, and $k$ is a positive integer, which has been recently studied in: On global attractivity of a higher order difference equation and its applications [Electron. J. Qual. Theory Diff. Equ. 2022, No. 2, 1–14]. We obtain some new sufficient conditions for the global attractivity of positive solutions of the equation, and show the applications of these results to some population models.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10913higher order nonlinear difference equationpositive equilibriumglobal attractivitypopulation model |
| spellingShingle | Xiao Wang Chuanxi Qian Global attractivity of a higher order nonlinear difference equation with decreasing terms Electronic Journal of Qualitative Theory of Differential Equations higher order nonlinear difference equation positive equilibrium global attractivity population model |
| title | Global attractivity of a higher order nonlinear difference equation with decreasing terms |
| title_full | Global attractivity of a higher order nonlinear difference equation with decreasing terms |
| title_fullStr | Global attractivity of a higher order nonlinear difference equation with decreasing terms |
| title_full_unstemmed | Global attractivity of a higher order nonlinear difference equation with decreasing terms |
| title_short | Global attractivity of a higher order nonlinear difference equation with decreasing terms |
| title_sort | global attractivity of a higher order nonlinear difference equation with decreasing terms |
| topic | higher order nonlinear difference equation positive equilibrium global attractivity population model |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10913 |
| work_keys_str_mv | AT xiaowang globalattractivityofahigherordernonlineardifferenceequationwithdecreasingterms AT chuanxiqian globalattractivityofahigherordernonlineardifferenceequationwithdecreasingterms |