Global Stability of a Rational Difference Equation
We consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive soluti...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2010/432379 |
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| author | Guo-Mei Tang Lin-Xia Hu Gang Ma |
| author_facet | Guo-Mei Tang Lin-Xia Hu Gang Ma |
| author_sort | Guo-Mei Tang |
| collection | DOAJ |
| description | We consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open problem introduced by Kulenović and Ladas in their monograph (see Kulenović and Ladas, 2002). |
| format | Article |
| id | doaj-art-bbef00027ff948bc91094a0f4ff5807f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-bbef00027ff948bc91094a0f4ff5807f2025-02-03T01:24:24ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2010-01-01201010.1155/2010/432379432379Global Stability of a Rational Difference EquationGuo-Mei Tang0Lin-Xia Hu1Gang Ma2School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, Gansu 730030, ChinaDepartment of Mathematics, Tianshui Normal University, Tianshui, Gansu 741001, ChinaSchool of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, Gansu 730030, ChinaWe consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open problem introduced by Kulenović and Ladas in their monograph (see Kulenović and Ladas, 2002).http://dx.doi.org/10.1155/2010/432379 |
| spellingShingle | Guo-Mei Tang Lin-Xia Hu Gang Ma Global Stability of a Rational Difference Equation Discrete Dynamics in Nature and Society |
| title | Global Stability of a Rational Difference Equation |
| title_full | Global Stability of a Rational Difference Equation |
| title_fullStr | Global Stability of a Rational Difference Equation |
| title_full_unstemmed | Global Stability of a Rational Difference Equation |
| title_short | Global Stability of a Rational Difference Equation |
| title_sort | global stability of a rational difference equation |
| url | http://dx.doi.org/10.1155/2010/432379 |
| work_keys_str_mv | AT guomeitang globalstabilityofarationaldifferenceequation AT linxiahu globalstabilityofarationaldifferenceequation AT gangma globalstabilityofarationaldifferenceequation |