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2012 On the Dynamics of a Higher-Order Rational Recursive Sequence
E. M. Elsayed
Commun. Math. Anal. 12(1): 117-133 (2012).

Abstract

In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence

\begin{equation*} x_{n+1}=ax_{n}+\dfrac{bx_{n-l}+cx_{n-k}}{dx_{n-l}+ex_{n-k}},\;\;\;n=0,1,..., \end{equation*}

where the parameters $a,b,c,d\;$and$\;e\;$are positive real numbers and the initial conditions $x_{-k},x_{-k+1},...,x_{-l},x_{-l+1},...,x_{-1}$ and $x_{0}\;$are positive real numbers.

Citation

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E. M. Elsayed. "On the Dynamics of a Higher-Order Rational Recursive Sequence." Commun. Math. Anal. 12 (1) 117 - 133, 2012.

Information

Published: 2012
First available in Project Euclid: 12 August 2011

zbMATH: 1235.39001
MathSciNet: MR2846206

Subjects:
Primary: 39A10

Rights: Copyright © 2012 Mathematical Research Publishers

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Vol.12 • No. 1 • 2012
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