The periodicity and solutions of the rational difference equation with periodic coefficients

Abstract

a b s t r a c tIn this paper, we give necessary and sufficient conditions for generalized solution and periodicity of the difference equationAlso, we obtain that the generalized solution is periodic with (k + 1)-period.

Global behavior of a three-dimensional system of difference equations of order three

“…Also, by using explicit forms of the solutions, they studied the asymptotic behavior of well-de…ned solutions of the system. For more works related to di¤erence equations and their two and three dimensional systems, see references [1,2,3,5,6,4,9,17,18,19,20,21,22,23,24,25,26,27,28,30,29,31,32,33,34]. In [7], El-Owaidy et al investigated global behavior of the di¤erence equation…”

Dynamics of the Rational Difference Equation $x_{n+1}=px_{n}+\frac{q}{x_{n-1}^2}$

“…In the past three decades, the research is rational difference equations has been significantly proceeded. We therefore do not feel to include basic textbook introductory materials as they are easily available in the references [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. We immediately proceed to the technicalities of the present rational difference equation which is of our interest.…”

The Solutions and Periods of Some Considered Non-Linear Difference Equation Systems

“…It is a fascinating issue because it is used to solve some problems that appear to be very complicated in applied areas. It has a wide application area especially in biology, physics, social and engineering fields [1][2][3][4][5][6][7][8][9]. Some are following.…”