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

Simple item page
dc.creatorBasu, Sukanya
dc.creatorMerino, Orlando
dc.date2008-12-17
dc.date.accessioned2026-07-07T12:16:18Z
dc.date.available2026-07-07T12:16:18Z
dc.descriptionFor nonnegative real numbers $α$, $β$, $γ$, $A$, $B$ and $C$ such that $B+C>0$ and $α+β+γ>0$, the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{α+βx_{n}+γx_{n-1}}{A+B x_{n}+C x_{n-1}}, \quad n=0,1,2,... %, \quad x_{-1},x_{0}\in [0,\infty) \end{equation*} has a unique positive equilibrium. A proof is given here for the following statements: \medskip \noindent Theorem 1. {\it For every choice of positive parameters $α$, $β$, $γ$, $A$, $B$ and $C$, all solutions to the difference equation \begin{equation*} x_{n+1}=\displaystyle\frac{α+βx_{n}+γx_{n-1}}{A+B x_{n}+C x_{n-1}}, \quad n=0,1,2,..., \quad x_{-1},x_{0}\in [0,\infty) \end{equation*} converge to the positive equilibrium or to a prime period-two solution.} \medskip \noindent Theorem 2. {\it For every choice of positive parameters $α$, $β$, $γ$, $A$, $B$ and $C$, all solutions to the difference equation \begin{equation*} x_{n+1}= \displaystyle\frac{α+βx_{n}+γx_{n-1}}{B x_{n}+C x_{n-1}}, \quad n=0,1,2,..., \quad x_{-1},x_{0}\in (0,\infty) \end{equation*} converge to the positive equilibrium or to a prime period-two solution.}
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/0812.3385
dc.identifierhttp://arxiv.org/abs/0812.3385
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/211762
dc.subjectDynamical Systems
dc.subject39A05; 39A11
dc.titleGlobal Behavior of Solutions to Two Classes of Second Order Rational Difference Equations
dc.typetext

Files

Collections

arXiv