scholarly journals Dynamics of System of Higher Order Difference Equations with Quadratic Terms

2020 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Related System ◽  
Order Difference ◽  
Initial Values

This paper aims to investigate the global asymptotic stability of following system of higher order difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-m}²)),y_{n+1}=A+B((x_{n})/(x_{n-m}²)) where A and B are positive numbers and the initial values are positive numbers. We also study the rate of convergence and oscillation behaviour of the solutions of related system.

scholarly journals Dynamics of a System of Higher Order Difference Equations with Quadratic Terms

2021 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Higher Order ◽  
Related System ◽  
Order Difference ◽  
Initial Values

In this paper we investigate the global asymptotic stability of following system ofhigher order difference equations with quadratic terms:xn+1=A+Byn/yn−m^2, yn+1=A+Bxn/xn−m^2, where A and B are positive numbers and the initial values are positive numbers.We also study the boundedness, rate of convergence and oscillation behaviour of thesolutions of related system.

scholarly journals On the Global Asymptotic Stability of A Two Dimensional System of Difference Equations with Quadratic Terms

2020 ◽  
Author(s):  
Erkan Taşdemir
Keyword(s):  
Asymptotic Stability ◽  
Rate Of Convergence ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Of Difference Equations ◽  
Related System ◽  
Initial Values ◽  
Two Dimensional System

In this paper, we study the global asymptotically stability of following system of difference equations with quadratic terms: x_{n+1}=A+B((y_{n})/(y_{n-1}²)),y_{n+1}=A+B((x_{n})/(x_{n-1}²)) where A and B are positive numbers and the initial values are positive numbers. We also investigate the rate of convergence and oscillation behaviour of the solutions of related system.

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 On the Global Asymptotic Stability of a Second-Order System of Difference Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Ibrahim Yalcinkaya
Keyword(s):  
Asymptotic Stability ◽  
Difference Equations ◽  
Global Asymptotic Stability ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
System Of Difference Equations ◽  
Initial Values

A sufficient condition is obtained for the global asymptotic stability of the following system of difference equations where the parameter and the initial values (for .

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 On a class of solvable higher-order difference equations

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 461-477 ◽  
Author(s):  
Stevo Stevic ◽  
Mohammed Alghamdi ◽  
Abdullah Alotaibi ◽  
Elsayed Elsayed
Keyword(s):  
Difference Equation ◽  
Closed Form ◽  
Difference Equations ◽  
Higher Order ◽  
Real Numbers ◽  
Order Difference ◽  
Initial Values ◽  
Long Term Behavior

Closed form formulas for well-defined solutions of the next difference equation xn = xn-2xn-k-2/xn-k(an + bnxn-2xn-k-2), n ? N0, where k ? N, (an)n?N0, (bn)n?N0, and initial values x-i, i = 1,k+2 are real numbers, are given. Long-term behavior of well-defined solutions of the equation when (an)n?N0 and (bn)n?N0 are constant sequences is described in detail by using the formulas. We also describe the domain of undefinable solutions of the equation. Our results explain and considerably improve some recent results in the literature.

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