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 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 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.

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.

Global behavior of a higher order difference equation

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
R. Abo-Zeid
Keyword(s):  
Difference Equation ◽  
Global Stability ◽  
Positive Solutions ◽  
Higher Order ◽  
Global Behavior ◽  
Real Numbers ◽  
Order Difference ◽  
Order Difference Equation ◽  
The Difference

AbstractThe aim of this paper is to investigate the global stability and periodic nature of the positive solutions of the difference equation $$x_{n + 1} = \frac{{A + Bx_{n - 2k - 1} }} {{C + D\prod\limits_{i = 1}^k {x_{n - 2i} } }}, n = 0,1,2, \ldots ,$$ where A, B are nonnegative real numbers, C,D > 0 and l, k are nonnegative integers such that l ≤ k.

scholarly journals Global Behavior of the Difference Equationxn+1=xn-1g(xn)

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Hongjian Xi ◽  
Taixiang Sun ◽  
Bin Qin ◽  
Hui Wu
Keyword(s):  
Continuous Function ◽  
Difference Equation ◽  
Positive Solution ◽  
Positive Solutions ◽  
Initial Conditions ◽  
Global Behavior ◽  
Initial Values ◽  
The Difference ◽  
Surjective Function

We consider the following difference equationxn+1=xn-1g(xn),n=0,1,…,where initial valuesx-1,x0∈[0,+∞)andg:[0,+∞)→(0,1]is a strictly decreasing continuous surjective function. We show the following. (1) Every positive solution of this equation converges toa,0,a,0,…,or0,a,0,a,…for somea∈[0,+∞). (2) Assumea∈(0,+∞). Then the set of initial conditions(x-1,x0)∈(0,+∞)×(0,+∞)such that the positive solutions of this equation converge toa,0,a,0,…,or0,a,0,a,…is a unique strictly increasing continuous function or an empty set.

scholarly journals Global Behavior of a Discrete Survival Model with Several Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Meirong Xu ◽  
Yuzhen Wang
Keyword(s):  
Difference Equation ◽  
Sufficient Conditions ◽  
Survival Model ◽  
Positive Equilibrium ◽  
Global Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
All Solutions ◽  
The Difference ◽  
Several Delays

The difference equationyn+1−yn=−αyn+∑j=1mβje−γjyn−kjis studied and some sufficient conditions which guarantee that all solutions of the equation are oscillatory, or that the positive equilibrium of the equation is globally asymptotically stable, are obtained.

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.

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