Authors: Stević, Stevo 
Iričanin, Bratislav
Šmarda, Zdeněk
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On a close to symmetric system of difference equations of second order
Journal: Advances in Difference Equations
Volume: 2015
Issue: 1
Issue Date: 29-Dec-2015
Rank: M22
ISSN: 1687-1847
DOI: 10.1186/s13662-015-0591-7
Closed form formulas of the solutions to the following system of difference equations:

xn=yn−1yn−2 / xn−1(an+bnyn−1yn−2),
yn=xn−1xn−2 / yn−1(αn+βnxn−1xn−2),
n ∈ N0,

where an, bn, αn, βn, n∈N0, and initial values x−i, y−i, i∈{1,2} are real numbers, are found. The domain of undefinable solutions to the system is described. The long-term behavior of its solutions is studied in detail for the case of constant an, bn, αn and βn, n∈N0.
Keywords: closed form solution | long-term behavior | periodic solutions | system of difference equations
Publisher: Springer Link
Project: Modulation of intracellular energy balance-controlling signalling pathways in therapy of cancer and neuro-immuno-endocrine disorders 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 
Physical and functional effects of radiation interaction with electrotechnical and biological systems 
European Regional Development Fund, Project CZ.1.05/1.1.00/02.0068
Brno University of Technology, Project FEKT-S-14-2200

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