On a Competitive System of Rational Difference Equations
This paper aims to investigate the global stability and the rate of convergence of positive solutions that converge to the equilibrium point of the system of difference equations in the modeling competitive populations in the form $$ x_{n+1}^{(1)}=\frac{\alpha x_{n-2}^{(1)}}{\beta +\gamma \prod\lim...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2019-12-01
|
| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/901893 |
| _version_ | 1797350223006138368 |
|---|---|
| author | Mehmet Gümüş |
| author_facet | Mehmet Gümüş |
| author_sort | Mehmet Gümüş |
| collection | DOAJ |
| description | This paper aims to investigate the global stability and the rate of convergence of positive solutions that converge to the equilibrium point of the system of difference equations in the modeling competitive populations in the form $$ x_{n+1}^{(1)}=\frac{\alpha x_{n-2}^{(1)}}{\beta +\gamma \prod\limits_{i=0}^{2}x_{n-i}^{(2)}},\text{ }x_{n+1}^{(2)}=\frac{\alpha _{1}x_{n-2}^{(2)}}{\beta _{1}+\gamma _{1}\prod\limits_{i=0}^{2}x_{n-i}^{(1)} }\text{, }n=0,1,... $$ where the parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1}$ are positive numbers and the initial conditions $ x_{-i}^{(1)},x_{-i}^{(2)}$ are arbitrary non-negative numbers for $i\in \{0,1,2\}$. |
| first_indexed | 2024-03-08T12:41:35Z |
| format | Article |
| id | doaj.art-abd7f68279494165b3e23e4b67fc286b |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:35Z |
| publishDate | 2019-12-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-abd7f68279494165b3e23e4b67fc286b2024-01-21T10:14:26ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532019-12-012422422810.32323/ujma.6491221225On a Competitive System of Rational Difference EquationsMehmet Gümüş0ZONGULDAK BÜLENT ECEVİT ÜNİVERSİTESİThis paper aims to investigate the global stability and the rate of convergence of positive solutions that converge to the equilibrium point of the system of difference equations in the modeling competitive populations in the form $$ x_{n+1}^{(1)}=\frac{\alpha x_{n-2}^{(1)}}{\beta +\gamma \prod\limits_{i=0}^{2}x_{n-i}^{(2)}},\text{ }x_{n+1}^{(2)}=\frac{\alpha _{1}x_{n-2}^{(2)}}{\beta _{1}+\gamma _{1}\prod\limits_{i=0}^{2}x_{n-i}^{(1)} }\text{, }n=0,1,... $$ where the parameters $\alpha ,\beta ,\gamma ,\alpha _{1},\beta _{1},\gamma _{1}$ are positive numbers and the initial conditions $ x_{-i}^{(1)},x_{-i}^{(2)}$ are arbitrary non-negative numbers for $i\in \{0,1,2\}$.https://dergipark.org.tr/tr/download/article-file/901893system of difference equationglobal asymptotic stabilityequilibriumrate of convergence |
| spellingShingle | Mehmet Gümüş On a Competitive System of Rational Difference Equations Universal Journal of Mathematics and Applications system of difference equation global asymptotic stability equilibrium rate of convergence |
| title | On a Competitive System of Rational Difference Equations |
| title_full | On a Competitive System of Rational Difference Equations |
| title_fullStr | On a Competitive System of Rational Difference Equations |
| title_full_unstemmed | On a Competitive System of Rational Difference Equations |
| title_short | On a Competitive System of Rational Difference Equations |
| title_sort | on a competitive system of rational difference equations |
| topic | system of difference equation global asymptotic stability equilibrium rate of convergence |
| url | https://dergipark.org.tr/tr/download/article-file/901893 |
| work_keys_str_mv | AT mehmetgumus onacompetitivesystemofrationaldifferenceequations |