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

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.

Anahtar Kelimeler:

Neural networks, GES, Lyapunov functional

The investigation of antioxidant and anticancer effects of some importance medical plants

For thousands of years, plants have been used for the treatment of many diseases. In addition, in modern pharmacy many plant compounds have an important place in the production of pharmaceutical raw materials or new medicines. The aim of this study was to determine the biological activity of extracts obtained from the fruits of the medical important bitter melon (Momordica charantia), pepino (Solanum muricatum) and goldenberry (Physalis peruviana). The total polyphenol content of the samples was measured spectrophotometrically using Folin-Ciocaltute reactivity. The DPPH free radical scavenging effect of plant samples was determined and antioxidant capacities were determined. In addition, the cytotoxic effects of the samples on human over and breast cancer cell lines (A2780 and MCF7, respectively) were determined using MTT method. As a result of the study, it was determined that the highest total polyphenol content was in the case of potency and the lowest content was in the case of pepino. All three plant samples revealed the effect of free radical elimination of DPPH dependent predation. Finally, it was determined that all three plant samples showed high cytotoxic effect on both human over and breast cancer cell lines. Results show us that in all three plant samples it has a significantly higher anticancer effect than antioxidant effect. With the extensive studies to be carried out after that, the mechanism of the effect can be enlightened and contribute to new treatment approaches.

Keywords:

Antioxidant, Cytotoxicity Momordica charantia, Physalis peruviana, Solanum muricatum,

PDF

___

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.