On a recursive sequence
Abstract
Purpose
The aim in this paper is to investigate the dynamics of difference equation yn+1=(pyn+yn−k)/(qyn+yn−k), n=0,1,2,… where k∈{1,2,3,…}, the initial conditions y−k, … ,y−1,y0 and the parameters p and q are non‐negative.
Design/methodology/approach
The paper studies characteristics such as the character of semicycles, periodicity and the global stability of the above mentioned difference equation.
Findings
In particular, the results solve the open problem introduced by Kulenovic and Ladas in their monograph, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures.
Originality/value
The global behaviour of the solutions of equation yn+1=(pyn+yn−k)/(qyn+yn−k), n=0,1,2,… were investigated providing valuable conclusions on practical data.
Keywords
Citation
Dehghan, M. and Mazrooei‐Sebdani, R. (2007), "On a recursive sequence", Kybernetes, Vol. 36 No. 1, pp. 98-115. https://doi.org/10.1108/03684920710741189
Publisher
:Emerald Group Publishing Limited
Copyright © 2007, Emerald Group Publishing Limited