On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$

Year 2023, Volume: 11 Issue: 1, 56 - 66, 28.03.2023

Mehmet Gümüş , Şeyma Irmak Eğilmez

https://doi.org/10.36753/mathenot.1243583

Cited By: 1

Abstract

In this paper, we aim to investigate the qualitative behavior of a general class of non-linear difference equations. That is, the prime period two solutions, the prime period three solutions and the stability character are examined. We also use a new technique introduced in [1] by E. M. Elsayed and later developed by O. Moaaz in [2] to examine the existence of periodic solutions of these general equations. Moreover, we use homogeneous functions for the investigation of the dynamics of the aforementioned equations.

Keywords

Homogeneous function, difference equation, periodicity, qualitative behavior, stability., Homogeneous function, difference equation, periodicity, qualitative behavior, stability.

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