Stability Analysis of a System of Exponential Difference Equations
We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: xn+1=(α1+β1e-xn+γ1e-xn-1)/(a1+b1yn+c1yn-1), yn+1=(α2+β2e-yn+γ2e-...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/375890 |
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| _version_ | 1832554051726737408 |
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| author | Q. Din K. A. Khan A. Nosheen |
| author_facet | Q. Din K. A. Khan A. Nosheen |
| author_sort | Q. Din |
| collection | DOAJ |
| description | We study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: xn+1=(α1+β1e-xn+γ1e-xn-1)/(a1+b1yn+c1yn-1), yn+1=(α2+β2e-yn+γ2e-yn-1)/(a2+b2xn+c2xn-1), where the parameters αi, βi, γi, ai, bi, and ci for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the positive equilibrium. Some numerical examples are given to verify our theoretical results. |
| format | Article |
| id | doaj-art-eb9833a435a542bea2897819227f1ac5 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-eb9833a435a542bea2897819227f1ac52025-02-03T05:52:34ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/375890375890Stability Analysis of a System of Exponential Difference EquationsQ. Din0K. A. Khan1A. Nosheen2Department of Mathematics, University of Poonch Rawalakot, Rawalakot 12350, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanWe study the boundedness character and persistence, existence and uniqueness of positive equilibrium, local and global behavior, and rate of convergence of positive solutions of the following system of exponential difference equations: xn+1=(α1+β1e-xn+γ1e-xn-1)/(a1+b1yn+c1yn-1), yn+1=(α2+β2e-yn+γ2e-yn-1)/(a2+b2xn+c2xn-1), where the parameters αi, βi, γi, ai, bi, and ci for i∈{1,2} and initial conditions x0, x-1, y0, and y-1 are positive real numbers. Furthermore, by constructing a discrete Lyapunov function, we obtain the global asymptotic stability of the positive equilibrium. Some numerical examples are given to verify our theoretical results.http://dx.doi.org/10.1155/2014/375890 |
| spellingShingle | Q. Din K. A. Khan A. Nosheen Stability Analysis of a System of Exponential Difference Equations Discrete Dynamics in Nature and Society |
| title | Stability Analysis of a System of Exponential Difference Equations |
| title_full | Stability Analysis of a System of Exponential Difference Equations |
| title_fullStr | Stability Analysis of a System of Exponential Difference Equations |
| title_full_unstemmed | Stability Analysis of a System of Exponential Difference Equations |
| title_short | Stability Analysis of a System of Exponential Difference Equations |
| title_sort | stability analysis of a system of exponential difference equations |
| url | http://dx.doi.org/10.1155/2014/375890 |
| work_keys_str_mv | AT qdin stabilityanalysisofasystemofexponentialdifferenceequations AT kakhan stabilityanalysisofasystemofexponentialdifferenceequations AT anosheen stabilityanalysisofasystemofexponentialdifferenceequations |