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 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 Global Behavior of Two Families of Nonlinear Symmetric Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Wanping Liu ◽  
Xiaofan Yang ◽  
Luxing Yang
Keyword(s):  
Asymptotic Stability ◽  
Recent Result ◽  
Positive Solutions ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Exponential Convergence ◽  
Higher Order ◽  
The Other ◽  
Global Behavior ◽  
Order Difference

We mainly investigate the global asymptotic stability and exponential convergence of positive solutions to two families of higher-order difference equations, one of which was recently studied in Stević's paper (2010). A new concise proof is given to a quite recent result by Stević and analogous parallel result of the other inverse equation, which extend related results of Aloqeili (2009), Berenhaut and Stević (2007), and Liao et al. (2009).

scholarly journals Global Behavior of a New Rational Nonlinear Higher-Order Difference Equation

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-4 ◽  
Author(s):  
Wen-Xiu Ma
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Global Asymptotic Stability ◽  
Nonnegative Integer ◽  
Equilibrium Solution ◽  
Higher Order ◽  
Positive Equilibrium ◽  
Global Behavior ◽  
Order Difference ◽  
Order Difference Equation

Let k be a nonnegative integer and c a real number greater than or equal to 1. We present qualitative global behavior of solutions to a rational nonlinear higher-order difference equation zn+1=(czn+zn-k+c-1znzn-k)/(znzn-k+c),  n≥0, with positive initial values z-k,z-k+1,⋯,z0, and show the global asymptotic stability of its positive equilibrium solution.

scholarly journals Global Behavior of a Higher-Order Difference Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-8
Author(s):  
Tuo Li ◽  
Xiu-Mei Jia
Keyword(s):  
Difference Equation ◽  
Higher Order ◽  
Positive Equilibrium ◽  
Global Behavior ◽  
Order Difference ◽  
Asymptotical Stable ◽  
Order Difference Equation

This paper is concerned with the global behavior of higher-order difference equation of the form , , Under some certain assumptions, it is proved that the positive equilibrium is globally asymptotical stable.

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