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

Year 2019, , 443 - 450, 28.06.2019

Yener Altun

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

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.
• Keadnarmol, P., Rojsiraphisal, T. (2014). Globally exponential stability of a certain neutral differential equation with time-varying delays. Adv. Difference Equ. 2014, 32, 10 pp.
• 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.
• Li, X. (2009). Global exponential stability for a class of neural networks. Appl. Math. Lett. 22, no. 8, 1235-1239.
• 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.
• Park, J. H. (2004). Delay-dependent criterion for asymptotic stability of a class of neutral equations. Appl. Math. Lett. 17, no. 10, 1203-1206.
• Park, J. H., Kwon, O. M. (2008). Stability analysis of certain nonlinear differential equation, Chaos Solitons Fractals, 37, 450-453.
• Tunç, C. (2015). Convergence of solutions of nonlinear neutral differential equations with multiple delays. Bol. Soc. Mat. Mex. (3) 21, 219-231.
• Tunç, C., Altun, Y. (2016). Asymptotic stability in neutral differential equations with multiple delays. J. Math. Anal. 7, no. 5, 40-53.
• Xu, S., Lam, J. (2006). A new approach to exponential stability analysis of neural networks with time-varying delays, Neural Netw., 19, 76-83.