scholarly journals Periodic solutions and stability of eighth order rational difference equations

2022 ◽  
Vol 26 (04) ◽  
pp. 405-417
Author(s):  
M. B. Almatrafi ◽  
M. M. Alzubaidi
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Eighth Order ◽  
Rational Difference Equations

scholarly journals Asymptotic Dynamics of a Class of Third Order Rational Difference Equations

2020 ◽  
Author(s):  
Sk Sarif Hassan ◽  
Soma Mondal ◽  
Swagata Mandal ◽  
Chumki Sau
Keyword(s):  
Periodic Solutions ◽  
Difference Equations ◽  
Real Line ◽  
Real Numbers ◽  
Positive Real ◽  
Third Order ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Asymptotic Dynamics ◽  
Positive Real Line

The asymptotic dynamics of the classes of rational difference equations (RDEs) of third order defined over the positive real-line as $$\displaystyle{x_{n+1}=\frac{x_{n}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-1}}{ax_n+bx_{n-1}+cx_{n-2}}}, \displaystyle{x_{n+1}=\frac{x_{n-2}}{ax_n+bx_{n-1}+cx_{n-2}}}$$ and $$\displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-1}}}, \displaystyle{x_{n+1}=\frac{ax_n+bx_{n-1}+cx_{n-2}}{x_{n-2}}}$$ is investigated computationally with theoretical discussions and examples. It is noted that all the parameters $a, b, c$ and the initial values $x_{-2}, x_{-1}$ and $x_0$ are all positive real numbers such that the denominator is always positive. Several periodic solutions with high periods of the RDEs as well as their inter-intra dynamical behaviours are studied.

On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers

2020 ◽  
Vol 70 (3) ◽  
pp. 641-656
Author(s):  
Amira Khelifa ◽  
Yacine Halim ◽  
Abderrahmane Bouchair ◽  
Massaoud Berkal
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
Fibonacci Numbers ◽  
Higher Order ◽  
Real Numbers ◽  
Lucas Numbers ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Fibonacci And Lucas Numbers

AbstractIn this paper we give some theoretical explanations related to the representation for the general solution of the system of the higher-order rational difference equations$$\begin{array}{} \displaystyle x_{n+1} = \dfrac{1+2y_{n-k}}{3+y_{n-k}},\qquad y_{n+1} = \dfrac{1+2z_{n-k}}{3+z_{n-k}},\qquad z_{n+1} = \dfrac{1+2x_{n-k}}{3+x_{n-k}}, \end{array}$$where n, k∈ ℕ0, the initial values x−k, x−k+1, …, x0, y−k, y−k+1, …, y0, z−k, z−k+1, …, z1 and z0 are arbitrary real numbers do not equal −3. This system can be solved in a closed-form and we will see that the solutions are expressed using the famous Fibonacci and Lucas numbers.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

scholarly journals On the Behavior of Solutions of the System of Rational Difference Equations: , , and

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Abdullah Selçuk Kurbanli
Keyword(s):  
Difference Equations ◽  
System Of Difference Equations ◽  
Rational Difference Equations

We investigate the solutions of the system of difference equations , , , where .

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