Dynamical Behavior of a Third-Order Difference Equation with Arbitrary Powers

Gümüs<br />Raafat Abo-Zeid<br />Özkan Öcalan

doi:10.5666/KMJ.2017.57.2.251

Article

Kyungpook Mathematical Journal 2017; 57(2): 251-263

Published online June 23, 2017

Dynamical Behavior of a Third-Order Difference Equation with Arbitrary Powers

Gümüs¹
Raafat Abo-Zeid²
Özkan Öcalan³

Department of Mathematics, Faculty of Science and Arts, Bülent Ecevit University, 67100, Zonguldak, Turkey¹
Department of Basic Sciences, The Egyptian Academy for Engineering and Advanced Technology, Cairo, Egypt²
Department of Mathematics, Faculty of Science and Arts, Akdeniz University, Antalya, Turkey³

Received: December 19, 2016; Accepted: May 4, 2017

Abstract

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Abstract

The aim of this paper is to investigate the dynamical behavior of the difference equation xn+1=αxnβ+γxn-1pxn-2q, n=0,1,…,

where the parameters α, β, γ, p, q are non-negative numbers and the initial values x₋₂,x₋₁, x₀ are positive numbers. Also, some numerical examples are given to verify our theoretical results.

Keywords: equilibrium point, global stability, periodicity, boundedness, solution