Stability analysis for a rational difference equation. Issue 1 (1st January 2020)

• Record Type: Journal Article
• Authors: Almatrafi, M. B.; Alzubaidi, Marwa M.
• Is Part Of: Arab journal of basic and applied sciences. Volume 27:Issue 1(2020)
• Page Start: 114
• Page End: 120
• Publication Date: 2020-01-01
• Subjects: Attractivity -- boundedness -- equilibrium -- recursive equation -- stability; 39A10; Science -- Arab countries -- Periodicals; Science -- Periodicals; Science; Arab countries; Periodicals; Electronic journals; 500
• DOI: 10.1080/25765299.2020.1726557
• Languages: English
• ISSNs: 2576-5299

Abstract

Abstract: Most qualitative behaviours of difference equations are rapidly investigated nowadays. This can be attributed to the fact that it is often sophisticated to construct the exact solutions of most difference equations. This article is written to analyse the local stability, global attractor and the boundedness of the solution of the seventh order difference equation given by x n + 1 = c 1 x n − 1 − c 2 x n − 1 x n − 4 c 3 x n − 4 + c 4 x n − 6, n = 0, 1, …, where the coefficients c i, for all i = 1, …, 4, are supposed to be positive real numbers and the initial conditions x i for all i = − 6, − 5, …, 0, are arbitrary non-zero real numbers. Under some suitable conditions, the stability, boundedness and a special case equation from the considered equation are presented in 2 D figures.