Stability analysis for a rational difference equation. Issue 1 (1st January 2020) - Almatrafi, M. B.; Alzubaidi, Marwa M.
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.