TY  - JOUR
AB  - 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.
VL  - 36
IS  - 1
SN  - 0368-492X
DO  - 10.1108/03684920710741189
UR  - https://doi.org/10.1108/03684920710741189
AU  - Dehghan Mehdi
AU  - Mazrooei‐Sebdani Reza
PY  - 2007
Y1  - 2007/01/01
TI  - On a recursive sequence
T2  - Kybernetes
PB  - Emerald Group Publishing Limited
SP  - 98
EP  - 115
Y2  - 2024/04/27
ER  -