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Dynamics of a Rational System of Difference Equations in the Plane

Abstract

We consider a rational system of first-order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of the system. In particular, we discuss the boundedness and the asymptotic behavior of the solutions, the existence of periodic solutions, and the stability of equilibria.

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Correspondence to Juan Perán.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bajo, I., Franco, D. & Perán, J. Dynamics of a Rational System of Difference Equations in the Plane. Adv Differ Equ 2011, 958602 (2011). https://doi.org/10.1155/2011/958602

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Asymptotic Behavior