2014
DOI: 10.22436/jnsa.007.06.02
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Asymptotic behavior of solutions of a rational system of difference equations

Abstract: We consider a two-dimensional autonomous system of rational difference equations with three positive parameters. It was conjectured by Ladas that every positive solution of this system converges to a finite limit. Here we confirm this conjecture.

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Cited by 4 publications
(4 citation statements)
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“…we have confirmed in [2] that [4, Conjecture 2.4 on page 1223] is true. Our goal here is to confirm another conjecture, in the case when By utilizing the relation…”
Section: Introductionsupporting
confidence: 64%
See 1 more Smart Citation
“…we have confirmed in [2] that [4, Conjecture 2.4 on page 1223] is true. Our goal here is to confirm another conjecture, in the case when By utilizing the relation…”
Section: Introductionsupporting
confidence: 64%
“…Rational systems of first-order difference equations in the plane have been receiving increasing attention in the last decade. Recently, in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] (see also the references therein), efforts have been made for a more systematic approach. In particular, the rational system…”
Section: Introductionmentioning
confidence: 99%
“…Our goal is to obtain a form of the solutions and the periodicity character of the systems of rational difference equations x n+1 = z n−3 a 1 + b 1 z n y n−1 x n−2 z n− 3 , y n+1 = x n−3 a 2 + b 2 x n z n−1 y n−2 x n−3 , z n+1 = y n−3 a 3 + b 3 y n x n−1 z n−2 y n− 3 , where the initial conditions are arbitrary real numbers. Also, the constants a i , b i , i = 1, 2, 3 are integer numbers.…”
Section: Introductionmentioning
confidence: 99%
“…Recently, there has been a great interest in studying nonlinear difference equations and systems , . One important reason for this is that some of the techniques that can be used in investigating equations arise in mathematical models describing real‐life situations in population biology, probability theory, genetics, number theory, economy, neural network, geometry, psychology, sociology, and so forth.…”
Section: Introductionmentioning
confidence: 99%