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

Mehmet Gümüş; Şeyma Irmak Eğilmez

doi:10.36753/mathenot.1243583

EN

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

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.

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Mehmet Gümüş ^*
0000-0002-7447-479X
Türkiye

Şeyma Irmak Eğilmez
0000-0003-1781-5399
Türkiye

Publication Date

March 28, 2023

Submission Date

January 27, 2023

Acceptance Date

March 11, 2023

Published in Issue

Year 2023 Volume: 11 Number: 1

DOI

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

IZ

https://izlik.org/JA87YA46KL

APA

Gümüş, M., & Eğilmez, Ş. I. (2023). On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$. Mathematical Sciences and Applications E-Notes, 11(1), 56-66. https://doi.org/10.36753/mathenot.1243583

AMA

1.Gümüş M, Eğilmez ŞI. On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$. Math. Sci. Appl. E-Notes. 2023;11(1):56-66. doi:10.36753/mathenot.1243583

Chicago

Gümüş, Mehmet, and Şeyma Irmak Eğilmez. 2023. “On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$”. Mathematical Sciences and Applications E-Notes 11 (1): 56-66. https://doi.org/10.36753/mathenot.1243583.

EndNote

Gümüş M, Eğilmez ŞI (March 1, 2023) On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$. Mathematical Sciences and Applications E-Notes 11 1 56–66.

IEEE

[1]M. Gümüş and Ş. I. Eğilmez, “On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$”, Math. Sci. Appl. E-Notes, vol. 11, no. 1, pp. 56–66, Mar. 2023, doi: 10.36753/mathenot.1243583.

ISNAD

Gümüş, Mehmet - Eğilmez, Şeyma Irmak. “On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$”. Mathematical Sciences and Applications E-Notes 11/1 (March 1, 2023): 56-66. https://doi.org/10.36753/mathenot.1243583.

JAMA

1.Gümüş M, Eğilmez ŞI. On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$. Math. Sci. Appl. E-Notes. 2023;11:56–66.

MLA

Gümüş, Mehmet, and Şeyma Irmak Eğilmez. “On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 1, Mar. 2023, pp. 56-66, doi:10.36753/mathenot.1243583.

Vancouver

1.Mehmet Gümüş, Şeyma Irmak Eğilmez. On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$. Math. Sci. Appl. E-Notes. 2023 Mar. 1;11(1):56-6. doi:10.36753/mathenot.1243583

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