scholarly journals Solution form of a higher-order system of difference equations and dynamical behavior of its special case

2016 ◽  
Vol 40 (10) ◽  
pp. 3599-3607 ◽  
Author(s):  
Nabila Haddad ◽  
Nouressadat Touafek ◽  
Julius Fergy T. Rabago
Keyword(s):  
Difference Equations ◽  
Dynamical Behavior ◽  
Higher Order ◽  
Order System ◽  
System Of Difference Equations ◽  
Solution Form ◽  
Special Case

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 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 Eventually Periodic Solutions of a Max-Type System of Difference Equations of Higher Order

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Guangwang Su ◽  
Taixiang Sun ◽  
Bin Qin
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Initial Conditions ◽  
Type System ◽  
Higher Order ◽  
System Of Difference Equations

We study in this paper the following max-type system of difference equations of higher order: xn=max{A,yn-k/xn-1} and yn=max{B,xn-k/yn-1}, n∈{0,1,2,…}, where A≥B>0, k≥1, and the initial conditions x-k,y-k,x-k+1,y-k+1,…,x-1,y-1∈(0,+∞). We show that (1) if AB>1, then every solution of the above system is periodic with period 2 eventually. (2) If AB=1>B, then every solution of the above system is periodic with period 2k or 2 eventually. (3) If A=B=1 or AB<1, then the above system has a solution which is not periodic eventually.

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 Global Dynamical Properties of Rational Higher-Order System of Difference Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
A. Q. Khan ◽  
S. M. Qureshi
Keyword(s):  
Numerical Simulation ◽  
Positive Solution ◽  
Higher Order ◽  
Order System ◽  
Discrete Time System ◽  
System Of Difference Equations ◽  
Time System ◽  
Dynamical Properties ◽  
Globally Stable ◽  
Theoretical Results

In this paper, global dynamical properties of rational higher-order system are explored in the interior of ℝ+3. It is explored that under certain parametric conditions, the discrete-time system has at most eight equilibria. By the method of linearization, local dynamics has been explored. It is explored that positive solution of the system is bounded, and moreover fixed point P000 is globally stable if α1/α2<1, α4/α5<1, α7/α8<1. It is also investigated that the positive solution of the system under consideration converges to P000. Lastly, theoretical results are confirmed by numerical simulation. The presented work is significantly extended and improves current results in the literature.

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