×

Global stability analysis in Cohen-Grossberg neural networks with delays and inverse Hölder neuron activation functions. (English) Zbl 1195.93124

Summary: A novel class of Cohen-Grossberg neural networks with delays and inverse Hölder neuron activation functions are presented. By using the topological degree theory and Linear Matrix Inequality (LMI) technique, the existence and uniqueness of equilibrium points for such Cohen-Grossberg neural networks are investigated. By constructing an appropriate Lyapunov function, a sufficient condition which ensures the global exponential stability of the equilibrium points is established. Two numerical examples are provided to demonstrate the effectiveness of the theoretical results.

MSC:

93D20 Asymptotic stability in control theory
92B20 Neural networks for/in biological studies, artificial life and related topics
34H10 Chaos control for problems involving ordinary differential equations

Software:

LMI toolbox
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Boyd, S.; Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory (1994), SIAM: SIAM Philadelphia, PA · Zbl 0816.93004
[2] Cohen, M. A.; Grossberg, S., Absolute stability and global pattern formation and parallel storage by competitive neural networks, IEEE Transactions on Systems, Man, and Cybernetics, 13, 815-826 (1983) · Zbl 0553.92009
[3] Cao, J.; Liang, J., Boundedness and stability for Cohen-Grossberg neural networks with time-varying delays, Journal of Mathematical Analysis and Applications, 296, 665-685 (2004) · Zbl 1044.92001
[4] Cao, J.; Li, X., Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach, Physica D, 212, 54-65 (2005) · Zbl 1097.34053
[5] Chen, Y., Global asymptotic stability of delayed Cohen-Grossberg neural networks, IEEE Transactions on Circuits and Systems I, 53, 351-357 (2006) · Zbl 1374.82019
[6] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0559.47040
[7] Gahinet, P.; Nemirovski, A.; Laub, J.; Chilali, M., LMI Control Toolbox-for Use With Matlab (1995), The MATH Works, Inc.: The MATH Works, Inc. Natick, MA
[8] Grossberg, S., Nonlinear neural networks principles, mechanisms, and architectures, Neural Networks, 1, 17-66 (1988)
[9] Huang, C., Dynamics of a class of Cohen-Grossberg neural networks with time-varying delays, Nonlinear Analysis: Real World Applications, 8, 40-52 (2007) · Zbl 1123.34053
[10] Huang, C.; He, Y.; Huang, L.; Zhu, W., \(P\) th moment stability analysis of stochastic recurrent neural networks with time-varying delays, Information Science, 178, 2194-2203 (2008) · Zbl 1144.93030
[11] Miller, P. K.; Michel, A. N., Differential Equations (1982), Academic: Academic New York
[12] Peng, C.; Tian, Y., Delay-dependent robust \(H_1\) control for uncertain systems with time-varying delay, Information Science, 179, 3187-3197 (2009) · Zbl 1171.93016
[13] Wang, L.; Zou, X., Exponential stability of Cohen-Grossberg neural networks, Neural Networks, 15, 415-422 (2002)
[14] Wongseree, W.; Chaiyaratana, N.; Vichittumaros, K.; Winichagoon, P.; Fucharoen, S., Thalassaemia classification by neural networks and genetic programming, Information Science, 177, 3, 771-786 (2007)
[15] Wu, H., Global stability analysis of a general class of discontinuous neural networks with linear growth activation functions, Information Science, 179, 3432-3441 (2009) · Zbl 1181.34063
[16] Wu, H.; Xue, X., Stability analysis for neural networks with inverse Lipschizan neuron activations and impulses, Applied Mathematical Modelling, 32, 11, 2347-2359 (2008) · Zbl 1156.34333
[17] Wu, H., Global exponential stability of Hopfiled neural networks with delays and inverse Lipschitz neuron activations, Nonlinear Analysis: Real World Applications, 10, 4, 2297-2306 (2009) · Zbl 1163.92308
[18] Wu, H.; Sun, J.; Zhong, X., Analysis of dynamical behaviour for delayed neural networks with inverse Lipschitzian neuron activations and impulses, International Journal of Innovative Computing, Information and Control, 4, 3, 705-715 (2008)
[19] Yang, X.; Huang, C.; Zhang, D.; Long, Y., Dynamic of Cohen-Grossberg neural networks with mixed delays and impulses, Abstract and Applied Analysis, 2008, 432341 (2008), (14 pages) · Zbl 1160.37431
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.