Stability analysis for a rational difference equation

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 nþ1 ¼ c 1 x nÀ1 À c2xnÀ1xnÀ4 c3xnÀ4þc4xnÀ6 , n ¼ 0, 1,. .. , where the coefficients c i , for all i ¼ 1,. .. , 4, are supposed to be positive real numbers and the initial conditions x i for all i ¼ À6, À5,. .. , 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.

On a Study of a Family of Higher-Order Recurrence Relations

“…It is now known that the Lie analysis method can be successfully used to solve ordinary difference equations, even in the case of systems of difference equations (see [1]). For more work, see [18][19][20][21][22].…”