On the Asymptotic Stability of the Nonlinear Difference Equation System

Serbun Ufuk Değer; Yaşar Bolat

doi:10.33187/jmsm.887537

EN

On the Asymptotic Stability of the Nonlinear Difference Equation System

Abstract

In this paper, we obtain some new results on the equi-boundedness of solutions and asymptotic stability for a class of nonlinear difference systems with variable delay of the form

x(n+1)=ax(n)+B(n)F(x(n−m(n))), n=0,1,2,...x(n+1)=ax(n)+B(n)F(x(n−m(n))),\ \ \ \ \ \ n=0,1,2,...

where

F

is the real valued vector function,

m : Z \to Z^{+},

which is bounded function and maximum value of

m

is

k

and

is a

k \times k

variable coefficient matrix. We carry out the proof of our results by using the Banach fixed point theorem and we use these results to determine the asymptotic stability conditions of an example.

Keywords

Asymptotic stability, Difference equation, Liapunov stable

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Serbun Ufuk Değer ^*
0000-0001-9458-8930
Türkiye

Yaşar Bolat
0000-0001-5215-427X
Türkiye

Publication Date

August 31, 2021

Submission Date

March 13, 2021

Acceptance Date

August 24, 2021

Published in Issue

Year 2021 Volume: 4 Number: 2

DOI

https://doi.org/10.33187/jmsm.887537

IZ

https://izlik.org/JA68UB47PR

APA

Değer, S. U., & Bolat, Y. (2021). On the Asymptotic Stability of the Nonlinear Difference Equation System. Journal of Mathematical Sciences and Modelling, 4(2), 65-71. https://doi.org/10.33187/jmsm.887537

AMA

1.Değer SU, Bolat Y. On the Asymptotic Stability of the Nonlinear Difference Equation System. Journal of Mathematical Sciences and Modelling. 2021;4(2):65-71. doi:10.33187/jmsm.887537

Chicago

Değer, Serbun Ufuk, and Yaşar Bolat. 2021. “On the Asymptotic Stability of the Nonlinear Difference Equation System”. Journal of Mathematical Sciences and Modelling 4 (2): 65-71. https://doi.org/10.33187/jmsm.887537.

EndNote

Değer SU, Bolat Y (August 1, 2021) On the Asymptotic Stability of the Nonlinear Difference Equation System. Journal of Mathematical Sciences and Modelling 4 2 65–71.

IEEE

[1]S. U. Değer and Y. Bolat, “On the Asymptotic Stability of the Nonlinear Difference Equation System”, Journal of Mathematical Sciences and Modelling, vol. 4, no. 2, pp. 65–71, Aug. 2021, doi: 10.33187/jmsm.887537.

ISNAD

Değer, Serbun Ufuk - Bolat, Yaşar. “On the Asymptotic Stability of the Nonlinear Difference Equation System”. Journal of Mathematical Sciences and Modelling 4/2 (August 1, 2021): 65-71. https://doi.org/10.33187/jmsm.887537.

JAMA

1.Değer SU, Bolat Y. On the Asymptotic Stability of the Nonlinear Difference Equation System. Journal of Mathematical Sciences and Modelling. 2021;4:65–71.

MLA

Değer, Serbun Ufuk, and Yaşar Bolat. “On the Asymptotic Stability of the Nonlinear Difference Equation System”. Journal of Mathematical Sciences and Modelling, vol. 4, no. 2, Aug. 2021, pp. 65-71, doi:10.33187/jmsm.887537.

Vancouver

1.Serbun Ufuk Değer, Yaşar Bolat. On the Asymptotic Stability of the Nonlinear Difference Equation System. Journal of Mathematical Sciences and Modelling. 2021 Aug. 1;4(2):65-71. doi:10.33187/jmsm.887537