scholarly journals Global behavior for a fourth-order rational difference equation

2005 ◽  
Vol 312 (2) ◽  
pp. 555-563 ◽  
Author(s):  
Xianyi Li
Keyword(s):  
Difference Equation ◽  
Fourth Order ◽  
Global Behavior ◽  
Rational Difference Equation

scholarly journals Global Asymptotic Stability for a Fourth-Order Rational Difference Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-7
Author(s):  
Meseret Tuba Gülpinar ◽  
Mustafa Bayram
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Fourth Order ◽  
Positive Equilibrium ◽  
Global Behavior ◽  
Asymptotically Stable ◽  
Nontrivial Solutions ◽  
Globally Asymptotically Stable ◽  
Rational Difference Equation ◽  
Positive Equilibrium Point

Our aim is to investigate the global behavior of the following fourth-order rational difference equation: , where and the initial values . To verify that the positive equilibrium point of the equation is globally asymptotically stable, we used the rule of the successive lengths of positive and negative semicycles of nontrivial solutions of the aforementioned equation.

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 The Dynamics of the Solutions of Some Difference Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
H. El-Metwally ◽  
R. Alsaedi ◽  
E. M. Elsayed
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Difference Equations ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Global Behavior ◽  
Local And Global Stability ◽  
Rational Difference Equation

This paper is devoted to investigate the global behavior of the following rational difference equation:yn+1=αyn-t/(β+γ∑i=0kyn-(2i+1)p∏i=0kyn-(2i+1)q),  n=0,1,2,…, whereα,β,γ,p,q∈(0,∞)andk,t∈{0,1,2,…}with the initial conditionsx0,  x-1,…,  x-2k,  x-2max {k,t}-1∈ (0,∞). We will find and classify the equilibrium points of the equations under studying and then investigate their local and global stability. Also, we will study the oscillation and the permanence of the considered equations.

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