Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1
Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the pa...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2017/1295089 |
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| _version_ | 1832553343288868864 |
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| author | Keying Liu Peng Li Weizhou Zhong |
| author_facet | Keying Liu Peng Li Weizhou Zhong |
| author_sort | Keying Liu |
| collection | DOAJ |
| description | Global dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the parameters space. The solution of the system converged to the equilibria or the boundary point (+∞,0) or (0,+∞) in each region depending on nonnegative initial conditions. These results completely described the behavior of the system. |
| format | Article |
| id | doaj-art-8e64642e40914c038628a5c64cadf77e |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-8e64642e40914c038628a5c64cadf77e2025-02-03T05:54:12ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2017-01-01201710.1155/2017/12950891295089Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1Keying Liu0Peng Li1Weizhou Zhong2School of Economics and Finance, Xi’an Jiaotong University, Xi’an 710061, ChinaSchool of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450045, ChinaSchool of Economics and Finance, Xi’an Jiaotong University, Xi’an 710061, ChinaGlobal dynamics of a system of nonlinear difference equations was investigated, which had five kinds of equilibria including isolated points and a continuum of nonhyperbolic equilibria along the coordinate axes. The local stability of these equilibria was analyzed which led to nine regions in the parameters space. The solution of the system converged to the equilibria or the boundary point (+∞,0) or (0,+∞) in each region depending on nonnegative initial conditions. These results completely described the behavior of the system.http://dx.doi.org/10.1155/2017/1295089 |
| spellingShingle | Keying Liu Peng Li Weizhou Zhong Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 Discrete Dynamics in Nature and Society |
| title | Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 |
| title_full | Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 |
| title_fullStr | Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 |
| title_full_unstemmed | Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 |
| title_short | Global Dynamics of Rational Difference Equations xn+1=xn+xn-1/q+ynyn-1 and yn+1=yn+yn-1/p+xnxn-1 |
| title_sort | global dynamics of rational difference equations xn 1 xn xn 1 q ynyn 1 and yn 1 yn yn 1 p xnxn 1 |
| url | http://dx.doi.org/10.1155/2017/1295089 |
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