Authors: Stević, Stevo 
Diblík, Josef
Iričanin, Bratislav
Šmarda, Zdeněk
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On the system of difference equations xn = xn - 1yn - 2ayn - 2 + byn - 1, yn = yn - 1xn - 2cxn - 2 + dxn - 1
Journal: Applied Mathematics and Computation
Volume: 270
First page: 688
Last page: 704
Issue Date: 1-Nov-2015
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2015.08.072
We show that the following system of difference equations xn=xn-1yn-2ayn-2+byn-1,yn=yn-1xn-2cxn-2+dxn-1,n∈N0, where parameters a, b, c, d, as well as initial values x-2,x-1,y-2,y-1, are real numbers, is solvable in closed form and by using obtained formulas we give some results on the long term behavior of their solutions. We also give natural explanations and considerably extend some recent results in the literature.
Keywords: Long term behavior | System of difference equations | System solved in closed form
Publisher: Elsevier
Project: Physical and functional effects of radiation interaction with electrotechnical and biological systems 
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 
CEITEC - Central European Institute of Technology, Project CZ.1.05/1.1.00/02.0068
Brno University of Technology, Project FEKT-S-14-2200

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