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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

Copyright

© S. Basu and O. Merino. 2009

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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