Global attractivity of a rational difference equation of order ten

Abstract

In this paper, we study qualitative properties and periodic nature of the solutions of the difference equationwhere the initial conditions x −9 , x −8 , x −7 , x −6 , x −5 , x −4 , x −3 , x −2 , x −1 , x 0 are arbitrary positive real numbers and a, b, c, d are constants. Also we obtain the form of solutions of some special cases of this equation.

Analysis of Some Dynamical Behaviors of a Sixth Order Difference Equation Ibraheem M. Alsulami and Elsayed M. Elsayed

“…Which gives by Theorem B in [13] that z is a global attractor of Eq.(1). Case(2): If α − βδv (γu−δv) 2 < 0 then from ( 8) and ( 9), the function g(u, v) is decreasing in u and increasing v.…”

On the dynamical behaviors and periodicity of difference equation of order three

“…For more linked results on this side can be found in [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27].…”

Global attractivity of a rational difference equation of order twenty

“…Difference equations are very simple in form but it is very difficult to understand the behavior of their solutions (Ahmed and Youssef, 2013;Alghamdi et al, 2013;Asiri et al, 2015;Das and Bayram, 2010;Din, 2015). Khaliq and Elsayed (2016) For other relevant work on difference equations see (Touafek and Haddad, 2015;Yazlik et al, 2014Yazlik et al, , 2015Zayed, 2014;Zhang et al, 2014). Suppose that is some interval of real numbers and a continuous function defined on +1 ( + 1 ), where is some natural number.…”