On Stability Analysis of Higher-Order Rational Difference Equation
In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0,∞, α, β, γ, δ∈0,∞, and r>p≥0. With initial val...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/3094185 |
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| _version_ | 1832566491954806784 |
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| author | Abdul Khaliq H. S. Alayachi M. S. M. Noorani A. Q. Khan |
| author_facet | Abdul Khaliq H. S. Alayachi M. S. M. Noorani A. Q. Khan |
| author_sort | Abdul Khaliq |
| collection | DOAJ |
| description | In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0,∞, α, β, γ, δ∈0,∞, and r>p≥0. With initial values w−p,w−p+1,…,w−r,w−r+1,…,w−1, and w0 are positive real numbers. Some numerical examples are given to verify our theoretical results. |
| format | Article |
| id | doaj-art-9283078e769f49fabc8a41d425a7af6b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-9283078e769f49fabc8a41d425a7af6b2025-02-03T01:04:01ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/30941853094185On Stability Analysis of Higher-Order Rational Difference EquationAbdul Khaliq0H. S. Alayachi1M. S. M. Noorani2A. Q. Khan3Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore Campus, PakistanSchool of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, Bangi Selangor, MalaysiaSchool of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, Bangi Selangor, MalaysiaDepartement of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, PakistanIn this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0,∞, α, β, γ, δ∈0,∞, and r>p≥0. With initial values w−p,w−p+1,…,w−r,w−r+1,…,w−1, and w0 are positive real numbers. Some numerical examples are given to verify our theoretical results.http://dx.doi.org/10.1155/2020/3094185 |
| spellingShingle | Abdul Khaliq H. S. Alayachi M. S. M. Noorani A. Q. Khan On Stability Analysis of Higher-Order Rational Difference Equation Discrete Dynamics in Nature and Society |
| title | On Stability Analysis of Higher-Order Rational Difference Equation |
| title_full | On Stability Analysis of Higher-Order Rational Difference Equation |
| title_fullStr | On Stability Analysis of Higher-Order Rational Difference Equation |
| title_full_unstemmed | On Stability Analysis of Higher-Order Rational Difference Equation |
| title_short | On Stability Analysis of Higher-Order Rational Difference Equation |
| title_sort | on stability analysis of higher order rational difference equation |
| url | http://dx.doi.org/10.1155/2020/3094185 |
| work_keys_str_mv | AT abdulkhaliq onstabilityanalysisofhigherorderrationaldifferenceequation AT hsalayachi onstabilityanalysisofhigherorderrationaldifferenceequation AT msmnoorani onstabilityanalysisofhigherorderrationaldifferenceequation AT aqkhan onstabilityanalysisofhigherorderrationaldifferenceequation |