Journal
AIMS MATHEMATICS
Volume 8, Issue 9, Pages 20561-20575Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.20231048
Keywords
nonlinear system of difference equations; solvable system; closed-form formula
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We consider a two-dimensional nonlinear system of difference equations with given delays and parameters, and find its general solution in detail.
We consider the two-dimensional nonlinear system of difference equations xn = xn-k ayn-l + byn-(k+l) cyn-l + dyn-(k+l) , yn = yn-k & alpha;xn-l + & beta;xn-(k+l) , & gamma;xn-l + & delta;xn-(k+l) for n E N0, where the delays k and l are two natural numbers, and the initial values x- j, y- j, 1 < j < k+l, and the parameters a, b, c, d, & alpha;, & beta;, & gamma;, & delta; are real numbers. We show that the system of difference equations is solvable by presenting a method for finding its general solution in detail. Bearing in mind that the system of equations is a natural generalization of the corresponding one-dimensional difference equation, whose special cases appear in the literature from time to time, our main result presented here also generalizes many results therein.
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