On periodicity of systems of rational difference equations

Volume 25, Issue 4, pp 381--390 http://dx.doi.org/10.22436/jmcs.025.04.08

Publication Date: August 12, 2021 Submission Date: June 04, 2021 Revision Date: June 29, 2021 Accteptance Date: July 13, 2021

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Authors

A. E. Hamza - Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia. N. Alsulami - Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.

Abstract

In this paper, we investigate the periodicity of two systems of rational sequences of second and third order, respectively. The systems include a permutation that gives the ability of changing the appearance of components of solutions in the equations of the systems. We find periods of systems in terms of the order of the permutation. The periodicity of two more systems of maximum type are studied. Finally, many illustrative examples are given.

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Keywords

• Systems of difference equations
• permutation groups
• periodicity

MSC

•  39A23

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