On the system of difference equations xn=xn−1yn−2ayn−2+byn−1,yn=yn−1xn−2cxn−2+dxn−1

Stevo Stević, Josef Diblík, Bratislav Iričanin and Zdeněk Šmarda

Applied Mathematics and Computation, 2015, vol. 270, issue C, 688-704

Abstract: 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: System of difference equations; System solved in closed form; Long term behavior (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:688-704

DOI: 10.1016/j.amc.2015.08.072

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