×

Global exponential robust stability of high-order Hopfield neural networks with S-type distributed time delays. (English) Zbl 1442.92003

Summary: By employing differential inequality technique and Lyapunov functional method, some criteria of global exponential robust stability for the high-order neural networks with S-type distributed time delays are established, which are easy to be verified with a wider adaptive scope.

MSC:

92B20 Neural networks for/in biological studies, artificial life and related topics
34K20 Stability theory of functional-differential equations
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Wen, S.; Zeng, Z.; Huang, T.; Zhang, Y., Exponential adaptive lag synchronization of memristive neural networks via fuzzy method and applications in pseudo random number generators, IEEE Transactions on Fuzzy Systems (2013)
[2] Cao, J.; Chen, G.; Li, P., Global synchronization in an array of delayed neural networks with hybrid coupling, IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, 38, 2, 488-498 (2008)
[3] Cao, J.; Xiao, M., Stability and Hopf bifurcation in a simplified BAM neural network with two time delays, IEEE Transactions on Neural Networks, 18, 2, 416-430 (2007)
[4] Wen, S.; Bao, G.; Zeng, Z.; Chen, Y.; Huang, T., Global exponential synchronization of memristor-based recurrent networks with time-varying delays, Neural Networks, 48, 195-203 (2013)
[5] Wen, S.; Zeng, Z.; Huang, T., Associative learning of integrate-and-fire neurons with memristor-based synapses, Neural Processing Letters, 38, 1, 69-80 (2013)
[6] Wallis, G., Stability criteria for unsupervised temporal association networks, IEEE Transactions on Neural Networks, 16, 2, 301-311 (2005)
[7] Wang, C.; Hill, D. J., Deterministic learning and rapid dynamical pattern recognition, IEEE Transactions on Neural Networks, 18, 3, 617-630 (2007)
[8] Liao, X.; Liao, Y., Stability of Hopfield-type neural networks II, Science in China A, 40, 8, 813-816 (1997) · Zbl 0886.68115
[9] Gopalsamy, K.; He, X. Z., Stability in asymmetric Hopfield nets with transmission delays, Physica D: Nonlinear Phenomena, 76, 4, 344-358 (1994) · Zbl 0815.92001
[10] Xu, D.; Zhao, H.; Zhu, H., Global dynamics of hopfield neural networks involving variable delays, Computers & Mathematics with Applications, 42, 1-2, 39-45 (2001) · Zbl 0990.34036
[11] Wang, Y.; Lin, P.; Wang, L., Exponential stability of reaction-diffusion high-order Markovian jump Hopfield neural networks with time-varying delays, Nonlinear Analysis: Real World Applications, 13, 3, 1353-1361 (2012) · Zbl 1239.93081
[12] Wang, Y.; Lu, C.; Ji, G.; Wang, L., Global exponential stability of high-order Hopfield-type neural networks with S-type distributed time delays, Communications in Nonlinear Science and Numerical Simulation, 16, 8, 3319-3325 (2011) · Zbl 1221.34204
[13] Hopfield, J. J., Neural networks and physical systems with emergent collective computational abilities, Proceedings of the National Academy of Sciences of the United States of America, 79, 8, 2554-2558 (1982) · Zbl 1369.92007
[14] Hopfield, J. J., Neurons with graded response have collective computational properties like those of two-state neurons, Proceedings of the National Academy of Sciences of the United States of America, 81, 10, 3088-3092 (1984) · Zbl 1371.92015
[15] Wang, L., Delayed Recurrent Neural Networks (2008), Beijing, China: Science Press, Beijing, China
[16] Civalleri, P. P.; Gilli, M.; Pandolfi, L., On stability of cellular neural networks with delay, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40, 3, 157-165 (1993) · Zbl 0792.68115
[17] Wen, S.; Zeng, Z.; Huang, T., H∞ filtering for neutral systems with mixed delays and multiplicative noises, IEEE Transactions on Circuits and Systems II: Express Briefs, 59, 11, 820-824 (2012)
[18] Wen, S.; Zeng, Z.; Huang, T., Exponential stability analysis of memristor-based recurrent neural networks with time-varying delays, Neurocomputing, 97, 233-240 (2012)
[19] Wen, S.; Zeng, Z.; Huang, T.; Li, C., Passivity and passification of stochastic impulsive memristor-based piecewise linear system with mixed delays, International Journal o f Robust and Nonlinear Control (2013) · Zbl 1312.93098
[20] Liao, X.; Fu, Y.; Gao, J.; Zhao, X., Stability of Hopfield neural networks with reaction-diffusion terms, Acta Electronica Sinica, 28, 1, 78-80 (2000)
[21] Song, Q.; Zhao, Z.; Li, Y., Global exponential stability of BAM neural networks with distributed delays and reaction-diffusion terms, Physics Letters A: General, Atomic and Solid State Physics, 335, 2-3, 213-225 (2005) · Zbl 1123.68347
[22] Wang, L.; Gao, Y., Global exponential robust stability of reaction-diffusion interval neural networks with time-varying delays, Physics Letters. A, 350, 5-6, 342-348 (2006) · Zbl 1195.35179
[23] Wang, L.; Xu, D., Asymptotic behavior of a class of reaction-diffusion equations with delays, Journal of Mathematical Analysis and Applications, 281, 2, 439-453 (2003) · Zbl 1031.35065
[24] Ruan, S.; Filfil, R. S., Dynamics of a two-neuron system with discrete and distributed delays, Physica D: Nonlinear Phenomena, 191, 3-4, 323-342 (2004) · Zbl 1049.92004
[25] Cao, J.; Yuan, K.; Li, H., Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays, IEEE Transactions on Neural Networks, 17, 6, 1646-1651 (2006)
[26] Wang, L.; Xu, D., Global asymptotic stability of bidirectional associative memory neural networks with S-type distributed delays, International Journal of Systems Science, 33, 11, 869-877 (2002) · Zbl 1047.68115
[27] Liu, P.; Yi, F.; Guo, Q.; Yang, J.; Wu, W., Analysis on global exponential robust stability of reaction-diffusion neural networks with S-type distributed delays, Physica D: Nonlinear Phenomena, 237, 4, 475-485 (2008) · Zbl 1139.35361
[28] Wang, L.; Zhang, R.; Wang, Y., Global exponential stability of reaction-diffusion cellular neural networks with S-type distributed time delays, Nonlinear Analysis: Real World Applications, 10, 2, 1101-1113 (2009) · Zbl 1167.35404
[29] Han, W.; Kao, Y.; Wang, L., Global exponential robust stability of static interval neural networks with S-type distributed delays, Journal of the Franklin Institute, 348, 8, 2072-2081 (2011) · Zbl 1242.34144
[30] Liu, X.; Wang, Q., Impulsive stabilization of high-order Hopfield-type neural networks with time-varying delays, IEEE Transactions on Neural Networks, 19, 1, 71-79 (2008)
[31] Xu, B.; Liu, X.; Liao, X., Global asymptotic stability of high-order Hopfield type neural networks with time delays, Computers & Mathematics with Applications, 45, 10-11, 1729-1737 (2003) · Zbl 1045.37056
[32] Brucoli, M.; Carnimeo, L.; Grassi, G., Associative memory design using discrete-time second-order neural networks with local interconnections, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 44, 2, 153-158 (1997) · Zbl 0874.68256
[33] Kosmatopoulos, E. B.; Christodoulou, M. A., Structural properties of gradient recurrent high-order neural networks, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 42, 9, 592-603 (1995) · Zbl 0943.68510
[34] Dembo, A.; Farotimi, O.; Kailath, T., High-order absolutely stable neural networks, IEEE transactions on circuits and systems, 38, 1, 57-65 (1991) · Zbl 0712.92002
[35] Hu, S., Nonlinear Analysis and Methods (1993), Wuhan, China: Huazhong University of Sci ence and Technology Press, Wuhan, China
[36] Guo, D.; Sun, J.; Liu, Z., Functional Methods of Nonlinear Ordinary Differential Equations (1995), Jinan, China: Shandong Science Press, Jinan, China
[37] Liao, X.; Chen, G.; Sanchez, E. N., L{MI}-based approach for asymptotically stability analysis of delayed neural networks, IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, 49, 7, 1033-1039 (2002) · Zbl 1368.93598
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.