scholarly journals Asymptotic Behavior of the Solutions of System of Difference Equations of Exponential Form

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Vu Van Khuong ◽  
Tran Hong Thai
Keyword(s):  
Asymptotic Behavior ◽  
Rate Of Convergence ◽  
Positive Solutions ◽  
Difference Equations ◽  
System Of Difference Equations ◽  
Positive Real ◽  
Exponential Form ◽  
Initial Values

The goal of this paper is to study the boundedness, the persistence, and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form: xn+1=a+be-yn+ce-xn/d+hyn, yn+1=a+be-xn+ce-yn/d+hxn, where a, b, c, d, and h are positive constants and the initial values x0, y0 are positive real values. Also, we determine the rate of convergence of a solution that converges to the equilibrium E=(x-,y-) of this system.

On some difference equations of exponential form

2018 ◽  
pp. 581-584
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
Real Numbers ◽  
Positive Real ◽  
Exponential Form ◽  
Numerical Examples

In this paper, the local asymptotic behavior of positive solutions of some exponential difference equations x_(n+1)=(x_n+x_(n-k))/(1+x_(n-k) e^(x_(n-k) ) ) , k ∈ N, n=0,1,2,… are investigated where the initial conditions are arbitrary positive real numbers. Furthermore, some numerical examples are presented to verify our results.

scholarly journals Global Character of a Six-Dimensional Nonlinear System of Difference Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Mehmet Gümüş ◽  
Yüksel Soykan
Keyword(s):  
Nonlinear System ◽  
Positive Solutions ◽  
Difference Equations ◽  
Dynamical Behavior ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Positive Real ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Global Character

The aim of this paper is to study the dynamical behavior of positive solutions for a system of rational difference equations of the following form:un+1=αun-1/β+γvn-2p,vn+1=α1vn-1/β1+γ1un-2p,n=0,1,…, where the parametersα,β,γ,α1,β1,γ1,pand the initial valuesu-i,v-ifori=0,1,2are positive real numbers.

Long-term behavior of positive solutions of an exponentially self-regulating system of difference equations

2017 ◽  
Vol 10 (03) ◽  
pp. 1750045 ◽  
Author(s):  
N. Psarros ◽  
G. Papaschinopoulos ◽  
K. B. Papadopoulos
Keyword(s):  
Asymptotic Behavior ◽  
Positive Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
System Of Difference Equations ◽  
Long Term Behavior

In this paper, we study the asymptotic behavior of the positive solutions of a system of the following difference equations: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] are positive constants and the initial conditions [Formula: see text] and [Formula: see text] are positive numbers.

scholarly journals Dynamics of a Higher-Order System of Difference Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Qi Wang ◽  
Qinqin Zhang ◽  
Qirui Li
Keyword(s):  
Positive Integer ◽  
Positive Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
Higher Order ◽  
Order System ◽  
Real Numbers ◽  
Precise Description ◽  
System Of Difference Equations ◽  
Positive Real

Consider the following system of difference equations:xn+1(i)=xn-m+1(i)/Ai∏j=0m-1xn-j(i+j+1)+αi,xn+1(i+m)=xn+1(i),x1-l(i+l)=ai,l,Ai+m=Ai,αi+m=αi,i,l=1,2,…,m;n=0,1,2,…,wheremis a positive integer,Ai,αi,i=1,2,…,m, and the initial conditionsai,l,i,l=1,2,…,m,are positive real numbers. We obtain the expressions of the positive solutions of the system and then give a precise description of the convergence of the positive solutions. Finally, we give some numerical results.

scholarly journals Qualitative study of a third order rational system of difference equations

2021 ◽  
Vol 25 (1) ◽  
pp. 81-97
Author(s):  
Mehmet Gümüş ◽  
Raafat Abo-Zeid
Keyword(s):  
Qualitative Study ◽  
Rate Of Convergence ◽  
Positive Solutions ◽  
Difference Equations ◽  
System Of Difference Equations ◽  
Third Order ◽  
Rational System ◽  
Numerical Examples ◽  
Rational Difference Equations ◽  
Zero Equilibrium

This paper is concerned with the dynamics of positive solutions for a system of rational difference equations of the following form un+1 = au2 n-1 b + gvn-2 , vn+1 = a1v 2 n-1 b1 + g1un-2 , n = 0, 1, . . . , where the parameters a, b, g, a1, b1, g1 and the initial values u-i, v-i ∈ (0, ∞), i = 0, 1, 2. Moreover, the rate of convergence of a solution that converges to the zero equilibrium of the system is discussed. Finally, some numerical examples are given to demonstrate the effectiveness of the results obtained.

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 On a solvable three-dimensional system of difference equations

Filomat ◽  
2020 ◽  
Vol 34 (4) ◽  
pp. 1167-1186
Author(s):  
Merve Kara ◽  
Yasin Yazlik
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Three Dimensional ◽  
Asymptotic Behavior Of Solutions ◽  
Dimensional System ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Initial Values ◽  
Forbidden Set ◽  
Three Dimensional System

In this paper, we show that the following three-dimensional system of difference equations xn = zn-2xn-3/axn-3 + byn-1, yn = xn-2yn-3/cyn-3 + dzn-1, zn = yn-2zn-3/ezn-3+ fxn-1, n ? N0, where the parameters a, b, c, d, e, f and the initial values x-i, y-i, z-i, i ? {1, 2, 3}, are real numbers, can be solved, extending further some results in literature. Also, we determine the asymptotic behavior of solutions and the forbidden set of the initial values by using the obtained formulas.

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