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: 17 August 2009

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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Authors’ Affiliations

(1)
Department of Mathematics, University of Rhode Island

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.