Applied Mathematics and Nonlinear Sciences
Journal license

Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 5, Issue 1


Published
on

March 31, 2020


Pages

275-282


DOI

Article

Solution of the Maximum of Difference Equation xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn} \matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}

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Authors

Dagistan Simsek Affiliation:
Kyrgyz Turkish Manas University, Bishkek, Kyrgyzstan.
, Burak Ogul Affiliation:
Kyrgyz Turkish Manas University, Bishkek, Kyrgyzstan.
and Fahreddin Abdullayev Affiliation:
Kyrgyz Turkish Manas University, Bishkek, Kyrgyzstan.


Abstract

In the recent years, there has been a lot of interest in studying the global behavior of, the socalled, max-type difference equations; see, for example, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. The study of max type difference equations has also attracted some attention recently. We study the behaviour of the solutions of the following system of difference equation with the max operator: paper deals with the behaviour of the solutions of the max type system of difference equations,
(1)

xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn},
\matrix{ {x_{n + 1} = max \left\{ {{A \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{A \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\},}}

where the parametr A and initial conditions x−1,x0, y−1,y0 are positive reel numbers.


Keywords

Difference equations, Periodicity, Max type difference equations, 39A10


Citation

Simsek, D., Ogul, B., & Abdullayev, F. (2020). Solution of the maximum of difference equation xn+1=max{Axn−1,ynxn};yn+1=max{Ayn−1,xnyn} \matrix{ {x_{n + 1} = max \left\{ {{a \over {x_{n - 1} }},{{y_n } \over {x_n }}} \right\};} & {y_{n + 1} = max \left\{ {{a \over {y_{n - 1} }},{{x_n } \over {y_n }}} \right\}}}. Applied Mathematics and Nonlinear Sciences, 5(1), 275–282. https://doi.org/10.2478/amns.2020.1.00025

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