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.

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.

Long-term behavior of positive solutions of a system of max-type difference equations

2014 ◽  
Vol 235 ◽  
pp. 567-574 ◽  
Author(s):  
Stevo Stević ◽  
Mohammed A. Alghamdi ◽  
Abdullah Alotaibi ◽  
Naseer Shahzad
Keyword(s):  
Positive Solutions ◽  
Difference Equations ◽  
Long Term Behavior

scholarly journals Periodic Solutions of a System of Nonlinear Difference Equations with Periodic Coefficients

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Durhasan Turgut Tollu
Keyword(s):  
Periodic Solution ◽  
Positive Solution ◽  
Periodic Solutions ◽  
Difference Equations ◽  
Real Numbers ◽  
Nonlinear Difference Equations ◽  
System Of Difference Equations ◽  
Positive Real ◽  
Long Term Behavior

This paper is dealt with the following system of difference equations x n + 1 = a n / x n + b n / y n , y n + 1 = c n / x n + d n / y n , where n ∈ ℕ 0 = ℕ ∪ 0 , the initial values x 0   and   y 0 are the positive real numbers, and the sequences a n n ≥ 0 , b n n ≥ 0 , c n n ≥ 0 , and d n n ≥ 0 are two-periodic and positive. The system is an extension of a system where every positive solution is two-periodic or converges to a two-periodic solution. Here, the long-term behavior of positive solutions of the system is examined by using a new method to solve the system.

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.

scholarly journals On the Solutions of the System of Difference Equationsxn+1=max{A/xn,yn/xn},yn+1=max{A/yn,xn/yn}

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Dağistan Simsek ◽  
Bilal Demir ◽  
Cengiz Cinar
Keyword(s):  
Difference Equations ◽  
Initial Conditions ◽  
Real Numbers ◽  
System Of Difference Equations ◽  
Positive Real

We study the behavior of the solutions of the following system of difference equationsxn+1=max⁡{A/xn,yn/xn},yn+1=max⁡{A/yn,xn/yn}where the constantAand the initial conditions are positive real numbers.

Visualising the invisible: performing chaos theory

Leonardo ◽  
2020 ◽  
pp. 1-8
Author(s):  
Emma Weitkamp
Keyword(s):  
Complex Systems ◽  
Chaos Theory ◽  
Initial Conditions ◽  
Starting Point ◽  
Weather And Climate ◽  
Butterfly Effect ◽  
Long Term Behavior ◽  
The Invisible

Edward Lorenz, the pioneering figure in the field of chaos theory coined the phrase “butterfly effect” and posed the famous question “Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?” In posing the question, Lorenz sought to highlight the intrinsic difficulty of predicting the long term behavior of complex systems that are sensitive to initial conditions, like, for example, the weather and climate; these systems are often referred to as chaotic. Taking Lorenz' butterfly as a starting point, Chaos Cabaret sought to explore the nuances of chaos theory through performance and music.

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