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Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations

Abstract

For nonnegative real numbers , , , , , and such that and , the difference equation , has a unique positive equilibrium. A proof is given here for the following statements: (1) For every choice of positive parameters, , , , , and , all solutions to the difference equation, converge to the positive equilibrium or to a prime period-two solution. (2) For every choice of positive parameters, , , , and , all solutions to the difference equation, converge to the positive equilibrium or to a prime period-two solution.

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Correspondence to Orlando Merino.

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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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Basu, S., Merino, O. Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations. Adv Differ Equ 2009, 128602 (2009). https://doi.org/10.1155/2009/128602

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Keywords

  • Differential Equation
  • Real Number
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis