Dynamics of positive solutions of a system of difference equations

2021 ◽  
Vol 392 ◽  
pp. 113489
Author(s):  
S. Abualrub ◽  
M. Aloqeili
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
System Of Difference Equations

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.

Existence of bounded positive solutions for a system of difference equations

2011 ◽  
Vol 218 (6) ◽  
pp. 2889-2912 ◽  
Author(s):  
Zeqing Liu ◽  
Liangshi Zhao ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
System Of Difference Equations

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 Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Zhijian Wei ◽  
Meitao Le
Keyword(s):  
Mathematical Models ◽  
Positive Solutions ◽  
Difference Equations ◽  
Epidemic Model ◽  
Sufficient Conditions ◽  
Nonlinear Difference Equations ◽  
System Of Difference Equations ◽  
Discrete Epidemic Model ◽  
Existence Of Positive Solutions

We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. Sufficient conditions are established that guarantee the existence of positive solutions, the existence of a unique nonnegative equilibrium, and the convergence of the positive solutions to the nonnegative equilibrium of the system of difference equations. The obtained results are new and they complement previously known 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.

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.

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