Dynamics of a Class of Higher Order Difference Equations
We prove that all positive solutions of the autonomous difference equation xn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, where k,m∈ℕ, and f is a continuous function satisfying the condition β min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um} for some β∈(0,1), converge to the positive equilibrium x¯=(α−1)/(β+1) if α&...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2007/73849 |
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| author | Bratislav D. Iricanin |
| author_facet | Bratislav D. Iricanin |
| author_sort | Bratislav D. Iricanin |
| collection | DOAJ |
| description | We prove that all positive solutions of the autonomous difference equation xn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, where k,m∈ℕ, and f is a continuous function satisfying the condition
β min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um} for some β∈(0,1), converge to the positive equilibrium x¯=(α−1)/(β+1) if α>1. |
| format | Article |
| id | doaj-art-aba247f10de6472da5a4a1be43e9124d |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-aba247f10de6472da5a4a1be43e9124d2025-02-03T01:27:28ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2007-01-01200710.1155/2007/7384973849Dynamics of a Class of Higher Order Difference EquationsBratislav D. Iricanin0Faculty of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, Beograd 11000, SerbiaWe prove that all positive solutions of the autonomous difference equation xn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, where k,m∈ℕ, and f is a continuous function satisfying the condition β min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um} for some β∈(0,1), converge to the positive equilibrium x¯=(α−1)/(β+1) if α>1.http://dx.doi.org/10.1155/2007/73849 |
| spellingShingle | Bratislav D. Iricanin Dynamics of a Class of Higher Order Difference Equations Discrete Dynamics in Nature and Society |
| title | Dynamics of a Class of Higher Order Difference Equations |
| title_full | Dynamics of a Class of Higher Order Difference Equations |
| title_fullStr | Dynamics of a Class of Higher Order Difference Equations |
| title_full_unstemmed | Dynamics of a Class of Higher Order Difference Equations |
| title_short | Dynamics of a Class of Higher Order Difference Equations |
| title_sort | dynamics of a class of higher order difference equations |
| url | http://dx.doi.org/10.1155/2007/73849 |
| work_keys_str_mv | AT bratislavdiricanin dynamicsofaclassofhigherorderdifferenceequations |