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

Authors : Mehmet GÜMÜŞ, Şeyma Irmak EĞİLMEZ

Pages : 56-66

Doi:10.36753/mathenot.1243583

View : 57 | Download : 12

Publication Date : 2023-03-28

Article Type : Research Paper

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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