scholarly journals Dynamics and Solutions’ Expressions of a Higher-Order Nonlinear Fractional Recursive Sequence

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Abeer Alshareef ◽  
Faris Alzahrani ◽  
Abdul Qadeer Khan
Keyword(s):  
Fixed Point ◽  
Difference Equation ◽  
Higher Order ◽  
Real Numbers ◽  
Stability Properties ◽  
Special Cases ◽  
Recursive Sequence ◽  
Rational Difference Equation

The principle purpose of this article is to examine some stability properties for the fixed point of the below rational difference equation U n + 1 = ξ U n − 8 + ε U n − 8 2 / μ U n − 8 + κ U n − 17 where ξ , ε , μ , and κ are arbitrary real numbers. Moreover, solutions for some special cases of the proposed difference equation are introduced.

On the global attractivity and the solution of recursive sequence

2010 ◽  
Vol 47 (3) ◽  
pp. 401-418 ◽  
Author(s):  
Elsayed Elsayed
Keyword(s):  
Difference Equation ◽  
Global Attractivity ◽  
Initial Conditions ◽  
Real Numbers ◽  
Positive Real ◽  
Special Cases ◽  
Recursive Sequence ◽  
The Difference

In this paper we study the behavior of the difference equation \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$x_{n + 1} = ax_{n - 2} + \frac{{bx_n x_{n - 2} }}{{cx_n + dx_{n - 3} }},n = 0,1,...$$ \end{document} where the initial conditions x−3 , x−2 , x−1 , x0 are arbitrary positive real numbers and a, b, c, d are positive constants. Also, we give the solution of some special cases of this equation.

scholarly journals Solution and Attractivity for a Rational Recursive Sequence

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
E. M. Elsayed
Keyword(s):  
Difference Equation ◽  
Initial Conditions ◽  
Specific Form ◽  
Nonlinear Difference Equation ◽  
Real Numbers ◽  
Positive Real ◽  
Special Cases ◽  
Recursive Sequence

This paper is concerned with the behavior of solution of the nonlinear difference equation , where the initial conditions , , are arbitrary positive real numbers and are positive constants. Also, we give specific form of the solution of four special cases of this equation.

scholarly journals On the Dynamics of a Higher-Order Rational Difference Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
A. M. Ahmed
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Real Numbers ◽  
Rational Difference Equation

The aim of this paper is to investigate the global asymptotic stability and the periodic character for the rational difference equationxn+1=αxn-1/(β+γΠi=lkxn-2ipi),  n=0,1,2,…, where the parametersα,β,γ,pl,pl+1,…,pkare nonnegative real numbers, andl,kare nonnegative integers such thatl≤k.

scholarly journals Qualitative Behavior of Rational Difference Equation of Big Order

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. M. El-Dessoky
Keyword(s):  
Global Convergence ◽  
Difference Equation ◽  
Initial Conditions ◽  
Qualitative Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Recursive Sequence ◽  
Rational Difference Equation

We investigate the global convergence, boundedness, and periodicity of solutions of the recursive sequencexn+1=axn-l+bxn-x/c+dxn-lxn-k,n=0,1,…,where the parametersa,  b,  c,anddare positive real numbers, and the initial conditionsx-t,x-t+1,…,x-1andx0are positive real numbers wheret=maxk,l.

scholarly journals Global behavior of a higher order rational difference equation

Filomat ◽  
2016 ◽  
Vol 30 (12) ◽  
pp. 3265-3276 ◽  
Author(s):  
R. Abo-Zeida
Keyword(s):  
Difference Equation ◽  
Initial Conditions ◽  
Higher Order ◽  
Global Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
All Solutions ◽  
Forbidden Set ◽  
Rational Difference Equation ◽  
The Difference

In this paper, we derive the forbidden set and discuss the global behavior of all solutions of the difference equation xn+1=Axn-k/B-C ?k,i=0 xn-i, n = 0,1,... where A,B,C are positive real numbers and the initial conditions x-k,..., x-1, x0 are real numbers.

scholarly journals Dynamics and Solutions of a Fifth-Order Nonlinear Difference Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-21 ◽  
Author(s):  
M. M. El-Dessoky ◽  
E. M. Elabbasy ◽  
Asim Asiri
Keyword(s):  
Difference Equation ◽  
Initial Conditions ◽  
Nonlinear Difference Equation ◽  
Real Numbers ◽  
Positive Real ◽  
Special Cases ◽  
Rational Difference Equation ◽  
Fifth Order

The main objective of this paper is to study the behavior of the rational difference equation of the fifth-order yn+1=αyn+βynyn-3/(Ayn-4+Byn-3), n=0,1,…, where α,β,A, and B are real numbers and the initial conditions y-4,y-3,y-2,y-1 and y0 are positive real numbers such that Ay-4+By-3≠0. Also, we obtain the solution of some special cases of this equation.

Dynamics of a higher-order rational difference equation

2006 ◽  
Vol 178 (2) ◽  
pp. 345-354 ◽  
Author(s):  
Mehdi Dehghan ◽  
Reza Mazrooei-Sebdani
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Rational Difference Equation

scholarly journals Boundedness of solutions and stability of certain second-order difference equation with quadratic term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Emin Bešo ◽  
Senada Kalabušić ◽  
Naida Mujić ◽  
Esmir Pilav
Keyword(s):  
Difference Equation ◽  
Initial Conditions ◽  
Second Order ◽  
Quadratic Term ◽  
Real Numbers ◽  
Positive Real ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Rational Difference Equation

AbstractWe consider the second-order rational difference equation $$ {x_{n+1}=\gamma +\delta \frac{x_{n}}{x^{2}_{n-1}}}, $$xn+1=γ+δxnxn−12, where γ, δ are positive real numbers and the initial conditions $x_{-1}$x−1 and $x_{0}$x0 are positive real numbers. Boundedness along with global attractivity and Neimark–Sacker bifurcation results are established. Furthermore, we give an asymptotic approximation of the invariant curve near the equilibrium point.

scholarly journals ON A HIGHER-ORDER RATIONAL DIFFERENCE EQUATION

2016 ◽  
Vol 34 (5_6) ◽  
pp. 369-382 ◽  
Author(s):  
FARIDA BELHANNACHE ◽  
NOURESSADAT TOUAFEK ◽  
RAAFAT ABO-ZEID
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Rational Difference Equation
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