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

Yener ALTUN (Van Yüzüncü Yıl Üniversitesi, Matematik Bölümü, Van, Türkiye)
Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
0 0
Yıl: 2019 Cilt: 8 Sayı: 2 Sayfa Aralığı: 443 - 450 Metin Dili: İngilizce İndeks Tarihi: 25-11-2020

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

Öz:
In this article, some novel approaches to the analysis of global exponential stability (GES) for a class of neuralnetworks with time-varying lags are presented. For functional differential equations, these approaches to are basedon Lyapunov stability theory. Then, the necessary and sufficient conditions for GES of the equation consideredhave been discussed. An example was given to illustrate the qualitative behavior of the solution of the proposedequation and MATLAB-Simulink Program was used to demonstrate the validity of the results obtained in thissample. Consequently, the obtained results include and improve the results found in the related literature.
Anahtar Kelime:

Zaman Değişken Gecikmelerle Sınıfsal Sinir Ağlarının Üstel Kararlılığı Üzerine Yeni Sonuçlar

Öz:
Bu makalede, zamanla değişen gecikmelerle sinir ağlarının bir sınıfı için global üstel kararlılığının analizine yönelik bazı yeni yaklaşımlar sunulmuştur. Fonksiyonel diferansiyel denklemlere yönelik bu yaklaşımlar için Lyapunov kararlılık teorisinden yararlanılmıştır. Daha sonra, dikkate alınan denklemin global üstel kararlılığı (GÜK) için gerek ve yeter koşullar tartışılmıştır. Önerilen denklemin çözümünün nitel davranışını göstermek için bir örnek verilmiştir ve bu örneklerde elde edilen sonuçların geçerliliğini göstermek için MATLAB-Simulink Programı kullanılmıştır. Sonuç olarak, elde edilen sonuçlar ilgili literatürde bulunan sonuçları içerir ve geliştirir.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • [1] Agarwal R.P., Grace S.R. 2000. Asymptotic stability of certain neutral differential equations. Math. Comput. Modelling, 31 (8-9): 9-15.
  • [2] Altun Y., Tunç C. 2017. On the global stability of a neutral differential equation with variable time-lags. Bull. Math. Anal. Appl., 9 (4): 31-41.
  • [3] Cakir M., Arslan D. 2015. The Adomian decomposition method and the differential transform method for numerical solution of multi-pantograph delay differential equations. Appl. Math., 6: 1332-1343.
  • [4] Cao J. 2001. Global exponential stability of Hopfield neural networks. Internat. J. Systems Sci., 32 (2): 233-236.
  • [5] El-Morshedy H.A., Gopalsamy K. 2000. Nonoscillation, oscillation and convergence of a class of neutral equations. Nonlinear Anal. Ser. A: Theory Methods, 40 (1-8):173-183.
  • [6] Erbe L., Kong Q., Zhang B. 1995. Oscillation Theory for Functional Differential Equations. Marcel Dekker, New York.
  • [7] Fridman E. 2002. Stability of linear descriptor systems with delays a Lyapunov-based approach. J. Math. Anal. Appl., 273 (1): 24-44.
  • [8] Gopalsamy K. 1992. Stability and Oscillation in Delay Differential Equations of Population Dynamics. Kluwer Academic, Netherlands.
  • [9] Gopalsamy K., Leung I., Liu P. 1998. Global Hopf-bifurcation in a neural netlet. Appl. Math. Comput., 94: 171-192.
  • [10] Keadnarmol P., Rojsiraphisal T. 2014. Globally exponential stability of a certain neutral differential equation with time-varying delays. Adv. Difference Equ., 32, 10 pp.
  • [11] Kulenovic M., Ladas G., Meimaridou A. 1987. Necessary and sufficient conditions for oscillations of neutral differential equations. J. Aust. Math. Soc. Ser. B, 28: 362-375.
  • [12] Li X. 2009. Global exponential stability for a class of neural networks. Appl. Math. Lett., 22 (8): 1235-1239.
  • [13] Mohamad S., Gopalsamy K. 2000. Dynamics of a class of discrete-time neural networks and their continuous-time counterparts. Math. Comput. Simulation, 53: 1-39.
  • [14] Park J.H. 2004. Delay-dependent criterion for asymptotic stability of a class of neutral equations. Appl. Math. Lett., 17 (10): 1203-1206.
  • [15] Park J.H., Kwon, O. M. 2008. Stability analysis of certain nonlinear differential equation. Chaos Solitons Fractals, 37: 450-453.
  • [16] Tunç C. 2015. Convergence of solutions of nonlinear neutral differential equations with multiple delays. Bol. Soc. Mat. Mex., 3 (21): 219-231.
  • [17] Tunç, C., Altun, Y. 2016. Asymptotic stability in neutral differential equations with multiple delays. J. Math. Anal., 7 (5): 40-53.
  • [18] Xu S., Lam J. 2006. A new approach to exponential stability analysis of neural networks with time-varying delays. Neural Netw., 19: 76-83.
APA ALTUN Y (2019). New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. , 443 - 450.
Chicago ALTUN Yener New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. (2019): 443 - 450.
MLA ALTUN Yener New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. , 2019, ss.443 - 450.
AMA ALTUN Y New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. . 2019; 443 - 450.
Vancouver ALTUN Y New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. . 2019; 443 - 450.
IEEE ALTUN Y "New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags." , ss.443 - 450, 2019.
ISNAD ALTUN, Yener. "New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags". (2019), 443-450.
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.
Chicago ALTUN Yener New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi 8, no.2 (2019): 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, 2019, ss.443 - 450.
AMA 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.
Vancouver 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.
IEEE ALTUN Y "New Results on the Exponential Stability of Class Neural Networks with Time-Varying Lags." Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, 8, ss.443 - 450, 2019.
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 (2019), 443-450.
Sayfa Oluşturulma Tarihi
23-04-2024 15:25

İLETİŞİM

TÜBİTAK ULAKBİM TR Dizin

Yüzüncüyıl, İşçi Blokları Mahallesi

Muhsin Yazıcıoğlu Caddesi No:51/C

06530 Çankaya / ANKARA +90 (312) 298 92 00

trdizin@tubitak.gov.tr

TÜBİTAK ULAKBİM Ulusal Akademik Ağ ve Bilgi Merkezi Cahit Arf Bilgi Merkezi © Tüm Hakları Saklıdır. Gizlilik Politikası Kullanım Şartları