Stability analysis of a discrete ecological model
In this paper, we study the qualitative behavior of following discrete-time population model: xn+1=a+bxn+rxn-1exp-y(n),yn-1=g+eyn+hyn-1exp-x(n), where parameters a, b, r, g, e, h and initial conditions x0, x-1, y0, y-1 are positive real numbers. More precisely, we investigate the existence and uniqu...
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| Format: | Article |
| Language: | English |
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International Academy of Ecology and Environmental Sciences
2014-06-01
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| Series: | Computational Ecology and Software |
| Subjects: | |
| Online Access: | http://www.iaees.org/publications/journals/ces/articles/2014-4(2)/stability-analysis-of-a-discrete-ecological-model.pdf |
| _version_ | 1818230096323936256 |
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| author | Q. Din E. M. Elsayed |
| author_facet | Q. Din E. M. Elsayed |
| author_sort | Q. Din |
| collection | DOAJ |
| description | In this paper, we study the qualitative behavior of following discrete-time population model: xn+1=a+bxn+rxn-1exp-y(n),yn-1=g+eyn+hyn-1exp-x(n), where parameters a, b, r, g, e, h and initial conditions x0, x-1, y0, y-1 are positive real numbers. More precisely, we investigate the existence and uniqueness of positive equilibrium point,boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium point of this model. Some numerical examples are given to verify our theoretical results. |
| first_indexed | 2024-12-12T10:29:04Z |
| format | Article |
| id | doaj.art-e4db55ee9c7e44488fa5f47e713451fd |
| institution | Directory Open Access Journal |
| issn | 2220-721X 2220-721X |
| language | English |
| last_indexed | 2024-12-12T10:29:04Z |
| publishDate | 2014-06-01 |
| publisher | International Academy of Ecology and Environmental Sciences |
| record_format | Article |
| series | Computational Ecology and Software |
| spelling | doaj.art-e4db55ee9c7e44488fa5f47e713451fd2022-12-22T00:27:25ZengInternational Academy of Ecology and Environmental SciencesComputational Ecology and Software2220-721X2220-721X2014-06-014289103Stability analysis of a discrete ecological modelQ. Din0E. M. Elsayed1Department of Mathematics, Faculty of Basic and Applied Sciences, University of PoonchRawalakot, PakistanDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia; Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptIn this paper, we study the qualitative behavior of following discrete-time population model: xn+1=a+bxn+rxn-1exp-y(n),yn-1=g+eyn+hyn-1exp-x(n), where parameters a, b, r, g, e, h and initial conditions x0, x-1, y0, y-1 are positive real numbers. More precisely, we investigate the existence and uniqueness of positive equilibrium point,boundedness character, persistence, local asymptotic stability, global behavior and rate of convergence of unique positive equilibrium point of this model. Some numerical examples are given to verify our theoretical results.http://www.iaees.org/publications/journals/ces/articles/2014-4(2)/stability-analysis-of-a-discrete-ecological-model.pdfpopulation modelsdifference equationssteady-statesboundednesslocal and global character |
| spellingShingle | Q. Din E. M. Elsayed Stability analysis of a discrete ecological model Computational Ecology and Software population models difference equations steady-states boundedness local and global character |
| title | Stability analysis of a discrete ecological model |
| title_full | Stability analysis of a discrete ecological model |
| title_fullStr | Stability analysis of a discrete ecological model |
| title_full_unstemmed | Stability analysis of a discrete ecological model |
| title_short | Stability analysis of a discrete ecological model |
| title_sort | stability analysis of a discrete ecological model |
| topic | population models difference equations steady-states boundedness local and global character |
| url | http://www.iaees.org/publications/journals/ces/articles/2014-4(2)/stability-analysis-of-a-discrete-ecological-model.pdf |
| work_keys_str_mv | AT qdin stabilityanalysisofadiscreteecologicalmodel AT emelsayed stabilityanalysisofadiscreteecologicalmodel |