应用数学学报(英文版)
HOME | ABOUT JOURNAL | EDITORIAL BOARD | FOR AUTHORS | SUBSCRIPTIONS | ADVERTISEMENT | CONTACT US
 
Acta Mathematicae Applicatae
Sinica, Chinese Series
 
   
   
Adv Search »  
Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :181-192    DOI: 10.1007/s10255-012-0133-y
ARTICLES Current Issue | Next Issue | Archive | Adv Search << | >>
Exponential Stability Analysis of Cohen-Grossberg Neural Networks with Time-varying Delays
Yi-min MENG, Li-hong HUANG, Zhao-hui YUAN
College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, China
Download: PDF (0KB)   HTML (1KB)   Export: BibTeX or EndNote (RIS)      Supporting Info
Abstract In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results.  
Service
Email this article
Add to my bookshelf
Add to citation manager
Email Alert
RSS
Articles by authors
Keywordsneural network   exponential stability   periodic solution   delay     
Abstract: In this paper, we study Cohen-Grossberg neural networks (CGNN) with time-varying delay. Based on Halanay inequality and continuation theorem of the coincidence degree, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of periodic solution. Our results complement previously known results.  
Keywordsneural network,   exponential stability,   periodic solution,   delay     
Received: 2008-02-20;
Fund:

Supported by the National Natural Science Foundation of China (No. 11071060) and Key Program of Application Science Foundation of Hunan Province (No. 2008FJ2008).

Corresponding Authors: Yi-min MENG     Email: mym2005cs@126.com
Cite this article:   
.Exponential Stability Analysis of Cohen-Grossberg Neural Networks with Time-varying Delays[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 181-192
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0133-y      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/181
 
[1] Arik, S. An analysis of exponential stability of delayed neural networks with time varying delays. Neural Networks, 17: 1027-1031 (2004)
[2] Arik, S. Stability analysis of delayed neural networks. IEEE Trans. Circuits Systems, 47: 1089-1092 (2000)
[3] Arik, S., Orman, Z. Global stability analysis of Cohen-Grossberg neural networks with time varying delays. Phys. Lett. A, 341: 410-421 (2005)
[4] Cao, J., Liang, J. Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. J. Math. Anal. Appl., 296: 665-685 (2004)
[5] Chen, T., Rong, L. Delay-independent stability analysis of Cohen-Grossberg neural networks. Phys. Lett. A, 317: 436-449 (2003)
[6] Chua, L.O., Yang, L. Cellular neural networks: Theory. IEEE Trans. Circuits Systems, 35: 1257-1272 (1988)
[7] Chua, L.O., Yang, L. Cellular neural networks: Applications. IEEE Trans. Circuits Systems, 35: 1273- 1290 (1988)
[8] Cohen, M.A., Grossberg, S. Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybernet, 13: 815-826 (1983)
[9] Gaines, R.E., Mawhin, J.L. Coincidence degree and nonlinear differential equations. Springer-Verlag, Berlin, 1977
[10] Gopalsamy, K. Stability and Oscillations in Delay Differential Equations of Population Dynamics. Kluwer Academic, Dordrecht, 1992
[11] Gopalsamy, K., He, X. Stability in asymmetric Hopfield nets with transmission delays. Phys. D, 76: 344-358 (1994)
[12] Hardy, G.H., Littlewood, J.E., Polya, G. Inequalities, second ed. Cambridge University Press, London, 1952
[13] Hwang, C., Chen, C., Liao, T. Globally exponential exponential stability of generalized Cohen-Grossberg neural networks with delays. Phys. Lett. A, 319: 157-166 (2003)
[14] Li, Y. Existence and stability of periodic solutions for Cohen-Grossberg neural networks with multiple delays. Chaos Solitons & Fractals, 20: 459-466 (2004)
[15] Li, X., Huang, L., Zhu, H. Global stability of cellular neural networks with constant and variable delays. Nonlinear Analysis, 53: 319-333 (2003)
[16] Liao, X., Li, C. LMI approach to asymptotical stability of multi-delayed neural networks. Phy. D, 200: 139-155 (2005)
[17] Liu, J. Global exponential stability of Cohen-Grossberg neural networks with time-varying delays. Chaos, Solitions and Fractals, 26: 935-945 (2005)
[18] Lu, W., Chen, T. New conditions on global stability of Cohen-Grossberg neural networks. Neural Comput., 15: 1173-1189 (2003)
[19] Ren, F., Cao, J. Periodic solutions for a class of higher-order Cohen-Grossberg type neural networks with delays. Computers and Mathematics with Applications, 54: 826-839 (2007)
[20] Roska, T., Wu, C., Chua, L.O. Stability of cellular neural networks with dominant nonlinear and delay-type templates. IEEE Trans. Circuits Systems, 40: 270-272 (1993)
[21] Song, Q., Zhao, Z. Global dissipativity of neural networks with both variable and unbounded delays. Chaos, Solitions and Fractals, 25: 393-401 (2005)
[22] Tu, F., Liao, X. Harmless delays for global asymptotic stability of Cohen-Grossberg neural network. Chaos, Solitions and Fractals, 26: 927-933 (2005)
[23] Wang, L., Zou, X. Exponential stability of Cohen-Grossberg neural networks. Neural Networks, 15: 415-422 (2002)
[24] Wang, L., Zou, X. Harmless delays in Cohen-Grossberg neural networks. Phys. D, 170: 162-173 (2002)
[25] Ye, H., Michel, A.N., Wang, K. Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. Phys. Rev. E, 51: 2611-2618 (1995)
[26] Yuan, Z., Yuan, L., Huang, L. Dynamics of periodic Cohen-Grossberg neural networks with varying delays. Neurocomputing, 70: 164-172 (2006)
[27] Yuan, Z., Huang, L., Hu, D., Dong, G. Existence and global exponential stability of periodic solution for Cohen-Grossberg neural networks with delays. Nonlinear Analysis (RWA), 7: 572-590 (2006)
[28] Yuan, K., Cao, J. Global exponential stability of Choen-Grossberg neural networks with multiple timevarying delays. Advances in Neural Networks-ISNN 2004, International symposium on neural networks, Dalian, China, Proceedings, August 2004, 78-83
[29] Yucel, E., Arik, S. New exponential stability results for delayed neural networks with time varying delays. Physica D, 191: 314-322 (2004)
没有找到本文相关文献
Copyright 2010 by Acta Mathematicae Applicatae Sinica, English Serie