Asymptotic behavior of Levin-Nohel nonlinear difference system with several delays

Mouataz Billah Mesmouli; Cemil Tunç; Taher S. Hassan; Hasan Nihal Zaidi; Adel A. Attiya; Mouataz Billah Mesmouli; Cemil Tunç; Taher S. Hassan; Hasan Nihal Zaidi; Adel A. Attiya

doi:10.3934/math.2024089

AIMS Mathematics

2024, Volume 9, Issue 1: 1831-1839. doi: 10.3934/math.2024089

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Asymptotic behavior of Levin-Nohel nonlinear difference system with several delays

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Campus, Turkey
3.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 07 November 2023 Revised: 05 December 2023 Accepted: 10 December 2023 Published: 14 December 2023
MSC : 39A30

In this manuscript, we considered a system of difference equations with delays and we established sufficient conditions to guarantee stability, asymptotic stability and exponential stability. In each type of stability, we created an appropriate space that guarantees us the existence of a fixed point that achieves the required stability.
- delay difference system,
- fixed points,
- fundamental matrix,
- asymptotic stability,
- exponential stability
Citation: Mouataz Billah Mesmouli, Cemil Tunç, Taher S. Hassan, Hasan Nihal Zaidi, Adel A. Attiya. Asymptotic behavior of Levin-Nohel nonlinear difference system with several delays[J]. AIMS Mathematics, 2024, 9(1): 1831-1839. doi: 10.3934/math.2024089

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Abstract

In this manuscript, we considered a system of difference equations with delays and we established sufficient conditions to guarantee stability, asymptotic stability and exponential stability. In each type of stability, we created an appropriate space that guarantees us the existence of a fixed point that achieves the required stability.

References

[1]	K. Ali Khelil, A. Ardjouni, A. Djoudi, Stability in linear delay Levin-Nohel difference equations, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. Math., 39 (2019), 1–12.
[2]	Y. Chitour, G. Mazanti, M. Sigalotti, Stability of non-autonomous difference equations with applications to transport and wave propagation on networks, Net. Heterog. Media, 11 (2016), 563–601. https://doi.org/10.3934/nhm.2016010 doi: 10.3934/nhm.2016010
[3]	J. Diblík, D. Y. Khusainov, J. Baštinec, A. S. Sirenko, Exponential stability of perturbed linear discrete systems, Adv. Differ. Equ., 2016 (2016), 2. https://doi.org/10.1186/s13662-015-0738-6 doi: 10.1186/s13662-015-0738-6
[4]	N. T. Dung, New stability conditions for mixed linear Levin-Nohel integro-differential equations, J. Math. Phys., 54 (2013), 082705. https://doi.org/10.1063/1.4819019 doi: 10.1063/1.4819019
[5]	N. T. Dung, On exponential stability of linear Levin-Nohel integro-differential equations, J. Math. Phys., 56 (2015), 022702. https://doi.org/10.1063/1.4906811 doi: 10.1063/1.4906811
[6]	N. T. Dung, A transfer theorem and stability of Levin-Nohel integro-differential equations, Adv. Differ. Equ., 2017 (2017), 70. https://doi.org/10.1186/s13662-017-1122-5 doi: 10.1186/s13662-017-1122-5
[7]	F. M. Hante, G. Leugering, T. I. Seidman, Modeling and analysis of modal switching in networked transport systems, Appl. Math. Optim., 59 (2009), 275–292. https://doi.org/10.1007/s00245-008-9057-6 doi: 10.1007/s00245-008-9057-6
[8]	M. B. Mesmouli, A. Ardjouni, A. Djoudi. Stability in nonlinear Levin-Nohel integro-differential equations, Nonlinear Stud., 22 (2015), 705–718.
[9]	M. B. Mesmouli, C. Tunç, Matrix measure and asymptotic behaviors of linear advanced systems of differential equations, Bol. Soc. Mat. Mex., 27 (2021), 56. https://doi.org/10.1007/s40590-021-00364-w doi: 10.1007/s40590-021-00364-w
[10]	M. B. Mesmouli, A. Ardjouni, A. Djoudi, Stability in nonlinear system of neutral difference equations with functional delay, Palestine J. Math., 5 (2016), 12–17.
[11]	M. B. Mesmouli, A. Ardjouni, A. Djoudi, Stability conditions for a mixed linear Levin-Nohel integro-differential system, J. Integral Equ. Appl., 34 (2022), 349–356. https://doi.org/10.1216/jie.2022.34.349 doi: 10.1216/jie.2022.34.349
[12]	M. B. Mesmouli, A. Ardjouni, N. Touafek, Stability of advanced nonlinear difference equations, Nonlinear Stud., 29 (2022), 927–934.
[13]	W. M. Oliva, C. Rocha, Reducible Volterra and Levin-Nohel retarded equations with infinite delay, J. Dyn. Diff. Equ., 22 (2010), 509–532. https://doi.org/10.1007/s10884-010-9177-y doi: 10.1007/s10884-010-9177-y
[14]	L. A. Pipes, Difference equations and their applications, Math. Mag., 32 (1959), 231–246.
[15]	E. J. P. G. Schmidt, On the modelling and exact controllability of networks of vibrating strings, SIAM J. Control Optim., 30 (1992), 229–245. https://doi.org/10.1137/0330015 doi: 10.1137/0330015
[16]	D. Zhao, S. Yuan, $3/2$-stability conditions for a class of Volterra-Levin equations, Nonlinear Anal. Theory Meth. Appl., 94 (2014), 1–11. https://doi.org/10.1016/j.na.2013.08.006 doi: 10.1016/j.na.2013.08.006

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