On a third-order system of difference equations

2012 ◽  
Vol 218 (14) ◽  
pp. 7649-7654 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Difference Equations ◽  
Order System ◽  
System Of Difference Equations ◽  
Third Order

scholarly journals On a Third-Order System of Difference Equations with Variable Coefficients

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Stevo Stević ◽  
Josef Diblík ◽  
Bratislav Iricanin ◽  
Zdenek Šmarda
Keyword(s):  
Asymptotic Behavior ◽  
Difference Equations ◽  
Variable Coefficients ◽  
Order System ◽  
Asymptotic Behavior Of Solutions ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Third Order ◽  
Initial Values ◽  
Explicit Formulae

We show that the system of three difference equationsxn+1=an(1)xn-2/(bn(1)ynzn-1xn-2+cn(1)),yn+1=an(2)yn-2/(bn(2)znxn-1yn-2+cn(2)), andzn+1=an(3)zn-2/(bn(3)xnyn-1zn-2+cn(3)),n∈N0, where all elements of the sequencesan(i),bn(i),cn(i),n∈N0,i∈{1,2,3}, and initial valuesx-j,y-j,z-j,j∈{0,1,2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced.

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 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 On a higher-order system of difference equations

2013 ◽  
pp. 1-18 ◽  
Author(s):  
Stevo Stevic ◽  
Mohammed Ali Alghamdi ◽  
Abdullah Alotaibi ◽  
Naseer Shahzad
Keyword(s):  
Difference Equations ◽  
Higher Order ◽  
Order System ◽  
System Of Difference Equations

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.

On a nonlinear second order system of difference equations

2013 ◽  
Vol 219 (24) ◽  
pp. 11388-11394 ◽  
Author(s):  
Stevo Stević ◽  
Mohammed A. Alghamdi ◽  
Abdullah Alotaibi ◽  
Naseer Shahzad
Keyword(s):  
Difference Equations ◽  
Second Order ◽  
Order System ◽  
System Of Difference Equations
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