New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags

Yener Altun

doi:10.17798/bitlisfen.488973

New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags

Abstract

In this article, some novel approaches to the analysis of globally exponential stability (GES) for a class of neural networks with time-varying lags are presented. These approaches to functional differential equations are based on Lyapunov stability theory. Then, the necessary and sufficient conditions for GES of the equation taking into account have been discussed. An example was given to illustrate the qualitative behavior of the solution of the proposed equation and MATLAB-Simulink Program was used to demonstrate the validity of the results obtained in these samples. Consequently, the obtained results include and improve the results found in the related literature.

Keywords

Neural networks,GES,Lyapunov functional

References

Agarwal, R. P., Grace, S. R. (2000). Asymptotic stability of certain neutral differential equations, Math. Comput. Modelling, 31, no. 8-9, 9–15.
Altun, Y., Tunç, C. (2017). On the global stability of a neutral differential equation with variable time-lags. Bull. Math. Anal. Appl. 9, no. 4, 31-41.
Cao, J. (2001). Global exponential stability of Hopfield neural networks, Internat. J. Systems Sci. 32, (2), 233-236.
El-Morshedy, H. A., Gopalsamy, K. (2000). Nonoscillation, oscillation and convergence of a class of neutral equations, Nonlinear Anal. 40, no. 1-8, Ser. A: Theory Methods, 173-183.
Erbe, L., Kong, Q., Zhang, B. (1995). Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York.
Fridman, E. (2002). Stability of linear descriptor systems with delays a Lyapunov-based approach. J. Math. Anal. Appl. 273, no. 1, 24-44.
Gopalsamy, K. (1992). Stability and Oscillation in Delay Differential Equations of Population Dynamics, Kluwer Academic, Netherlands.
Gopalsamy, K., Leung, I., Liu, P. (1998). Global Hopf-bifurcation in a neural netlet, Appl. Math. Comput. 94, 171-192.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Yener Altun ^*
0000-0003-1073-5513
Türkiye

Publication Date

June 28, 2019

Submission Date

November 28, 2018

Acceptance Date

March 29, 2019

Published in Issue

Year 2019 Volume: 8 Number: 2

DOI

https://doi.org/10.17798/bitlisfen.488973

IZ

https://izlik.org/JA27AD42CE

Cite

RIS / Bibtex

APA

Altun, Y. (2019). New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 8(2), 443-450. https://doi.org/10.17798/bitlisfen.488973

AMA

1.Altun Y. New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2019;8(2):443-450. doi:10.17798/bitlisfen.488973

Chicago

Altun, Yener. 2019. “New Results on the Exponential Stability of Class Neural Networks With Time-Varying Lags”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 8 (2): 443-50. https://doi.org/10.17798/bitlisfen.488973.

EndNote

Altun Y (June 1, 2019) New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 8 2 443–450.

IEEE

[1]Y. Altun, “New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 8, no. 2, pp. 443–450, June 2019, doi: 10.17798/bitlisfen.488973.

ISNAD

Altun, Yener. “New Results on the Exponential Stability of Class Neural Networks With Time-Varying Lags”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 8/2 (June 1, 2019): 443-450. https://doi.org/10.17798/bitlisfen.488973.

JAMA

1.Altun Y. New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2019;8:443–450.

MLA

Altun, Yener. “New Results on the Exponential Stability of Class Neural Networks With Time-Varying Lags”. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 8, no. 2, June 2019, pp. 443-50, doi:10.17798/bitlisfen.488973.

Vancouver

1.Yener Altun. New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi. 2019 Jun. 1;8(2):443-50. doi:10.17798/bitlisfen.488973