Global behavior of two third order rational difference equations with quadratic terms

Abstract

In this paper, we determine the forbidden sets, introduce an explicit formula for the solutions and discuss the global behaviors of solutions of the difference equations $$\begin{array}{} \displaystyle x_{n+1}=\frac{ax_{n}x_{n-1}}{bx_{n-1}+ cx_{n-2}},\quad n=0,1,\ldots \end{array} $$ where a,b,c are positive real numbers and the initial conditions x−2,x−1,x0 are real numbers.

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

“…By incorporating recent advancements in theoretical analysis and numerical validation techniques, our study pushes the boundaries of understanding in this domain and opens up new avenues for exploration. While Abo-Zeid [17] provides explicit solutions for specific difference equations, our paper explores the fundamental properties of systems of difference equations representing different analytical challenges. Our work provides a deeper analysis of the behavior of bidimensional systems, while Abo-Zeid's [17] work revolves around studying the details of explicit solutions and the general behavior of specific models.…”

On the Solutions of a Fourth Order Difference Equation

“…where the parameters A and p are positive real numbers. For more on difference equations (See [3]- [7], [9], [11]- [14], [16]- [23]) and the references therein.…”

Behaviors of the Solutions via Their Closed-Form Formulas for Two Rational Third-Order Difference Equations

“…In [1][2][3][4][5], the first author ( [1] together with Kamal) solved and studied the solutions for the difference equations…”

“…Motivated by [27], we shall solve, find the forbidden set, and study (∀ positive real values of α, β, c ) global behavior of the admissible solutions for equations (3) and (4) where α, β, c are positive real numbers and x − 3 , x − 2 , x − 1 , x 0 are nonzero real numbers.…”