Behavior of a Competitive System of Second-Order Difference Equations
We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: xn+1=(α1+β1xn-1)/(a1+b1yn), yn+1=(α2+β2yn-1)/(...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/283982 |
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| _version_ | 1832558777709101056 |
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| author | Q. Din T. F. Ibrahim K. A. Khan |
| author_facet | Q. Din T. F. Ibrahim K. A. Khan |
| author_sort | Q. Din |
| collection | DOAJ |
| description | We study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: xn+1=(α1+β1xn-1)/(a1+b1yn), yn+1=(α2+β2yn-1)/(a2+b2xn), where the parameters αi, βi, ai, and bi for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. Some numerical examples are given to verify our theoretical results. |
| format | Article |
| id | doaj-art-161ef193bda848969910aee17b459360 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-161ef193bda848969910aee17b4593602025-02-03T01:31:31ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/283982283982Behavior of a Competitive System of Second-Order Difference EquationsQ. Din0T. F. Ibrahim1K. A. Khan2Department of Mathematics, Faculty of Basic and Applied Sciences, University of Poonch Rawalakot, Rawalakot 12350, PakistanDepartment of Mathematics, Faculty of Sciences and Arts (S.A.), King Khalid University, Abha, Sarat Abida 61914, Saudi ArabiaDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanWe study the boundedness and persistence, existence, and uniqueness of positive equilibrium, local and global behavior of positive equilibrium point, and rate of convergence of positive solutions of the following system of rational difference equations: xn+1=(α1+β1xn-1)/(a1+b1yn), yn+1=(α2+β2yn-1)/(a2+b2xn), where the parameters αi, βi, ai, and bi for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. Some numerical examples are given to verify our theoretical results.http://dx.doi.org/10.1155/2014/283982 |
| spellingShingle | Q. Din T. F. Ibrahim K. A. Khan Behavior of a Competitive System of Second-Order Difference Equations The Scientific World Journal |
| title | Behavior of a Competitive System of Second-Order Difference Equations |
| title_full | Behavior of a Competitive System of Second-Order Difference Equations |
| title_fullStr | Behavior of a Competitive System of Second-Order Difference Equations |
| title_full_unstemmed | Behavior of a Competitive System of Second-Order Difference Equations |
| title_short | Behavior of a Competitive System of Second-Order Difference Equations |
| title_sort | behavior of a competitive system of second order difference equations |
| url | http://dx.doi.org/10.1155/2014/283982 |
| work_keys_str_mv | AT qdin behaviorofacompetitivesystemofsecondorderdifferenceequations AT tfibrahim behaviorofacompetitivesystemofsecondorderdifferenceequations AT kakhan behaviorofacompetitivesystemofsecondorderdifferenceequations |