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  • Research Article
  • Open Access

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

Advances in Difference Equations20092009:128602

https://doi.org/10.1155/2009/128602

  • Received: 9 December 2008
  • Accepted: 7 July 2009
  • Published:

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.

Keywords

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

Publisher note

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Authors’ Affiliations

(1)
Department of Mathematics, University of Rhode Island, Kingston, RI 02881, USA

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