On the periodicity of the solution of a rational difference equation

Authors : A. M. ALOTAİBİ, M. S. M. NOORANİ, M. A. EL-MONEAM

Pages : 1427-1434

Doi:10.31801/cfsuasmas.535865

View : 12 | Download : 7

Publication Date : 2019-08-01

Article Type : Research Paper

Abstract :In this paper, some cases on the periodicity of the rational difference equation S_{n+1}=S_{n-p}insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(insert ignore into journalissuearticles values(aS_{n-q}+bS_{n-r}+cS_{n-s});/insert ignore into journalissuearticles values(dS_{n-q}+eS_{ n-r}+fS_{n-s});););, are investigated, where a, b, c, d, e, f ∈insert ignore into journalissuearticles values(0,∞);. The initial conditions S_{-p}, S_{-p+1},...,S_{-q},  S_{-q+1},...,S_{-r},  S_{-r+1},...,S_{-s},...,S_{-s+1},...,S₋₁ and S₀ are arbitrary positive real numbers such that p>q>r>s≥0. Some numerical examples are provided to illustrate the theoretical discussion.
Keywords : Rational difference equations, periodicity, higher order