Monotone and oscillatory solutions of a rational difference equation containing quadratic terms

We show that the second order rational difference equation has several qualitatively different types of positive solutions. Depending on the non-negative parameter values A,B,C,α,β, all solutions may converge to 0, or they may all be unbounded. For some parameter values both cases can occur, or coex...

Full description

Saved in:
Bibliographic Details
Published in:Journal of difference equations and applications 2008-10, Vol.14 (10-11), p.1045-1058
Main Authors: Dehghan, M., Kent, C.M., Mazrooei-Sebdani, R., Ortiz, N.L., Sedaghat, H.
Format: Article
Language:English
Subjects:
monotonic
non-monotonic
period two
quadratic
rational
semiconjugate
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that the second order rational difference equation has several qualitatively different types of positive solutions. Depending on the non-negative parameter values A,B,C,α,β, all solutions may converge to 0, or they may all be unbounded. For some parameter values both cases can occur, or coexist depending on the initial values. We find converging solutions of both monotonic and oscillatory types, as well as periodic solutions with period two. A semiconjugate relation facilitates derivations of these results by providing a link to a rational first order equation.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190802332266