Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays

Nonlinear Analysis: Real World Applications

Volumn 9, Issue 2, 2008, Pages 500-510

  Song, Qiankun ^a   Zhang, Jiye ^b  

^a CHONGQING JIAOTONG UNIVERSITY   (China)

^b SOUTHWEST JIAOTONG UNIVERSITY   (China)

Author keywords

Cohen Grossberg neural network; Global exponential stability; Impulsive; M matrix; Time varying delays

Indexed keywords

ASYMPTOTIC STABILITY; LYAPUNOV FUNCTIONS; MATHEMATICAL MODELS; TIME DELAY; TIME VARYING SYSTEMS;

COHEN-GROSSBERG NEURAL NETWORK; GLOBAL EXPONENTIAL STABILITY; INEQUALITY TECHNIQUES; TIME VARYING DELAYS;

NEURAL NETWORKS;

EID: 37249055492     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2006.11.015     Document Type: Article

References (26)

1. Akca H., Alassar R., Covachev V., Covacheva Z., and Al-Zahrani E. Continuous-time additive Hopfield-type neural networks with impulses. J. Math. Anal. Appl. 290 2 (2004) 436-451
2. Cao J.D., and Liang J.L. Boundedness and stability for Cohen-Grossberg neural network with time-varying delays. J. Math. Anal. Appl. 296 (2004) 665-685
3. Chen T.P., and Rong L.B. Delay-independent stability analysis of Cohen-Grossberg neural networks. Phys. Lett. A 317 (2003) 436-449
4. Chen T.P., and Rong L.B. Robust global exponential stability of Cohen-Grossberg neural networks with time delays. IEEE Trans. Neural Networks 15 (2004) 203-206
5. Cohen M.A., and Grossberg S. Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13 (1983) 815-826
6. Forti M., and Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans. Circuits Syst. I 42 (1995) 354-366
7. Gopalsamy K. Stability of artificial neural networks with impulses. Appl. Math. Comput. 154 (2004) 783-813
8. Guan Z.H., and Chen G.R. On delayed impulsive Hopfield neural networks. Neural Networks 12 (1999) 273-280
9. Guan Z.H., Lam J., and Chen G.R. On impulsive autoassociative neural networks. Neural Networks 13 (2000) 63-69
10. Huang C.X., and Huang L.H. Dynamics of a class of Cohen-Grossberg neural networks with time-varying delays. Nonlinear Anal. R. World Appl. 8 (2007) 40-52
11. Hwang C.C., Cheng C.J., and Liao T.L. Globally exponential stability of generalized Cohen-Grossberg neural networks with delays. Phys. Lett. A 319 (2003) 157-166
12. Li Y.K. Existence and stability of periodic solutions for Cohen-Grossberg neural networks. Phys. Lett. A 317 (2003) 436-449
13. Li Y.K., and Lu L.H. Global exponential stability and existence of periodic solution of Hopfield-type neural networks with impulses. Phys. Lett. A 333 (2004) 62-71
14. Liao X.F., Li C.G., and Wong K.W. Criteria for exponential stability of Cohen-Grossberg neural networks. Neural Networks 17 (2004) 1401-1414
15. Lu W.L., and Chen T.P. New conditions on global stability of Cohen-Grossberg neural networks. Neural Comput. 15 (2003) 1173-1189
16. Marcus C.M., and Westervelt R.M. Stability of analog neural networks with delay. Phys. Rev. A 39 (1989) 347-359
17. Minc H. Nonnegative matrices (1988), Wiley, NewYork
18. Roska T., and Chua L.O. Cellular neural networks with nonlinear and delay-type template elements nonuniform grids. Int. J. Circuit Theory Appl. 20 (1992) 469-481
19. Wang L., and Zou X.F. Harmless delays in Cohen-Grossberg neural networks. Physica D 170 (2002) 162-173
20. Wang L., and Zou X.F. Exponential stability of Cohen-Grossberg neural networks. Neural Networks 15 (2002) 415-422
21. Xu D.Y., and Yang Z.C. Impulsive delay differential inequality and stability of neural networks. J. Math. Anal. Appl. 305 (2005) 107-120
22. Ye H., Michel A.N., and Wang K.N. Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. Phys. Rev. E 51 (1995) 2611-2618
23. Zhang J.Y. Global stability analysis in Hopfield neural networks. Appl. Math. Lett. 16 (2003) 925-931
24. Zhang J.Y., Suda Y., and Komine H. Global exponential stability of Cohen-Grossberg neural networks with variable delays. Phys. Lett. A 338 (2005) 44-50
25. Zhang Y., and Sun J.T. Stability of impulsive neural networks with time delays. Phys. Lett. A 348 (2005) 44-50
26. Zhao H.Y., and Wang L. Hopf bifurcation in Cohen-Grossberg neural network with distributed delays. Nonlinear Anal. R. World Appl. 8 (2007) 73-89