Some real life problems are modeled using difference equations. Extracting the exact solutions of such equations is an active topic for some scientists. This paper investigates the equilibrium points, stability, boundedness, periodicity, and some exact solutions for eighth order rational difference equations. The exact solutions are obtained using the iterations method. We also present some 2D figures to show the validity of the obtained results. The used methods can be applied for other nonlinear difference equations.
Some difference equations are generally studied by investigating their long behaviours rather than their exact solutions. The proposed equations cannot be solved analytically. Hence, this article discusses the main qualitative behaviours of two rational difference equations. Some appropriate hypotheses are examined and given to show the local and global attractivity. Special cases from the considered equations are solved analytically. The periodicity is also proved in this work. We also illustrate the achieved results in some 2D figures.
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.
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