scholarly journals Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17
Author(s):  
Xiu-Mei Jia ◽  
Wan-Tong Li
Keyword(s):  
Difference Equation ◽  
Global Attractor ◽  
Positive Solutions ◽  
Local Stability ◽  
Global Attractivity ◽  
Initial Conditions ◽  
Higher Order ◽  
Nonlinear Difference Equation ◽  
Positive Equilibrium ◽  
Prime Period

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: , , where the parameters and the initial conditions . We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.

scholarly journals On the Rational Recursive Sequence

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
E. M. E. Zayed ◽  
A. B. Shamardan ◽  
T. A. Nofal
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Global Attractor ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Positive Equilibrium ◽  
Real Numbers ◽  
Recursive Sequence ◽  
Boundedness Character ◽  
The Difference

We study the global stability, the periodic character, and the boundedness character of the positive solutions of the difference equation , , in the two cases: (i) ; (ii) , where the coefficients and, and the initial conditions are real numbers. We show that the positive equilibrium of this equation is a global attractor with a basin that depends on certain conditions posed on the coefficients of this equation.

scholarly journals On a Higher-Order Nonlinear Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Bratislav D. Iričanin
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Higher Order ◽  
Nonlinear Difference Equation

This paper shows that all positive solutions of a higher-order nonlinear difference equation are bounded, extending some recent results in the literature.

scholarly journals Global Behavior of a Higher Order Fuzzy Difference Equation

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 938
Author(s):  
Guangwang Su ◽  
Taixiang Sun ◽  
Bin Qin
Keyword(s):  
Difference Equation ◽  
Positive Solutions ◽  
Higher Order ◽  
Positive Equilibrium ◽  
Global Behavior ◽  
Convergence Behavior

Our aim in this paper is to investigate the convergence behavior of the positive solutions of a higher order fuzzy difference equation and show that all positive solutions of this equation converge to its unique positive equilibrium under appropriate assumptions. Furthermore, we give two examples to account for the applicability of the main result of this paper.

scholarly journals Global Stability of a Rational Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Guo-Mei Tang ◽  
Lin-Xia Hu ◽  
Gang Ma
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Stability ◽  
Positive Solutions ◽  
Open Problem ◽  
Global Asymptotic Stability ◽  
Initial Conditions ◽  
Nonlinear Difference Equation ◽  
Real Numbers ◽  
Rational Difference Equation

We consider the higher-order nonlinear difference equation with the parameters, and the initial conditions are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In particular, our results solve the open problem introduced by Kulenović and Ladas in their monograph (see Kulenović and Ladas, 2002).

scholarly journals Dynamics of a Class of Higher Order Difference Equations

2007 ◽  
Vol 2007 ◽  
pp. 1-6
Author(s):  
Bratislav D. Iricanin
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Positive Solutions ◽  
Difference Equations ◽  
Higher Order ◽  
Positive Equilibrium ◽  
Order Difference

We prove that all positive solutions of the autonomous difference equationxn=αxn−k/(1+xn−k+f(xn−1,…,xn−m)), n∈ℕ0, wherek,m∈ℕ, andfis a continuous function satisfying the conditionβ min{u1,…,um}≤f(u1,…,um)≤β max{u1,…,um}for someβ∈(0,1), converge to the positive equilibriumx¯=(α−1)/(β+1)ifα>1.

scholarly journals Dynamics of a Higher-Order Nonlinear Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Guo-Mei Tang ◽  
Lin-Xia Hu ◽  
Xiu-Mei Jia
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Initial Conditions ◽  
Higher Order ◽  
Nonlinear Difference Equation ◽  
Asymptotically Stable ◽  
Unique Equilibrium ◽  
Real Numbers ◽  
Positive Real ◽  
Globally Asymptotically Stable

We consider the higher-order nonlinear difference equation , , where parameters are positive real numbers and initial conditions are nonnegative real numbers, . We investigate the periodic character, the invariant intervals, and the global asymptotic stability of all positive solutions of the abovementioned equation. We show that the unique equilibrium of the equation is globally asymptotically stable under certain conditions.

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