Results 1 to 10 of about 4,643,635 (279)
Analytical Solution to a Third-Order Rational Difference Equation [PDF]
The Scientific World Journal, 2023 Inspired by some open conjectures in a rational dynamical system by G. Ladas and Palladino, in this paper, we consider the problem of solving a third-order difference equation. We comment the conjecture by Ladas.
Alvaro H. Salas S. +2 more
doaj +3 more sources
On a Conjecture for a Higher-Order Rational Difference Equation [PDF]
Advances in Difference Equations, 2009 This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation xn=(∏j=1m(xn−kj+1)+∏j=1m(xn−kj−1))/(∏j=1m(xn−kj+1)−∏j=1m(xn− ...
Maoxin Liao, Xianhua Tang, Changjin Xu
doaj +5 more sources
Dynamics of a Rational Difference Equation [PDF]
Advances in Difference Equations, 2010 The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn+1=(α+βxn+γxn-k)/(1+xn-k), n∈ℕ0, where the parameters
Wan-Tong Li, Lin-Xia Hu, Xiu-Mei Jia
doaj +4 more sources
On A System of Rational Difference Equation
Demonstratio Mathematica, 2014 In this paper, we study local asymptotic stability, global character and periodic nature of solutions of the system of rational difference equations given by xn+1= , yn=, n=0, 1,…, where the parameters a; b; c; d; e; f ∊ (0; ∞), and with initial ...
Din Qamar
doaj +3 more sources
Global Stability of a Rational Difference Equation [PDF]
Discrete Dynamics in Nature and Society, 2010 We consider the higher-order nonlinear difference equation 𝑥𝑛+1=(𝑝+𝑞𝑥𝑛−𝑘)/(1+𝑥𝑛+𝑟𝑥𝑛−𝑘),𝑛=0,1,… with the parameters, and the initial conditions 𝑥−𝑘,…,𝑥0 are nonnegative real numbers.
Guo-Mei Tang, Lin-Xia Hu, Gang Ma
doaj +6 more sources
Dynamical behavior of one rational fifth-order difference equation
Karpatsʹkì Matematičnì Publìkacìï, 2023 In this paper, we study the qualitative behavior of the rational recursive equation \begin{equation*} x_{n+1}=\frac{x_{n-4}}{\pm1\pm x_{n}x_{n-1}x_{n-2}x_{n-3}x_{n-4}}, \quad n \in \mathbb{N}_{0}:=\{0\}\cup\mathbb N, \end{equation*} where the initial ...
B. Ogul, D. Simsek
doaj +1 more source
Stability analysis for a rational difference equation
Arab Journal of Basic and Applied Sciences, 2020 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
M. B. Almatrafi, Marwa M. Alzubaidi
doaj +1 more source
On the Solutions of Three-Dimensional Rational Difference Equation Systems
Journal of Mathematics, 2021 In this paper, we are interested in a technique for solving some nonlinear rational systems of difference equations of third order, in three-dimensional case as a special case of the following system:xn+1=ynzn−1/yn±xn−2,yn+1=znxn−1/zn±yn−2, and zn+1=xnyn−
H. S. Alayachi +2 more
doaj +1 more source
On Stability Analysis of Higher-Order Rational Difference Equation
Discrete Dynamics in Nature and Society, 2020 In this paper, we study the equilibrium points, local asymptotic stability of equilibrium points, global behavior of equilibrium points, boundedness and periodicity of the rational recursive sequence wn+1=wn−pα+βwn/γwn+δwn−r, where γwn≠−δwn−r for r∈0 ...
Abdul Khaliq +3 more
doaj +1 more source
On a Rational $(P+1)$th Order Difference Equation with Quadratic Term
Universal Journal of Mathematics and Applications, 2022 In this paper, we derive the forbidden set and determine the solutions of the difference equation that contains a quadratic term \begin{equation*} x_{n+1}=\frac{x_{n}x_{n-p}}{ax_{n-(p-1)}+bx_{n-p}},\quad n\in\mathbb{N}_0, \end{equation*} where the ...
R Abo-zeıd, Messaoud Berkal
doaj +1 more source