Exponential stability of reaction-diffusion generalized Cohen-Grossberg neural networks with time-varying delays

Chaos, Solitons and Fractals

Volumn 32, Issue 5, 2007, Pages 1713-1719

  Zhou, Qinghua ^a   Wan, Li ^a,b   Sun, Jianhua ^a  

^a NANJING UNIVERSITY   (China)

^b ZHEJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DELAY CONTROL SYSTEMS; FUNCTIONS; NEURAL NETWORKS; PARAMETER ESTIMATION; TIME VARYING CONTROL SYSTEMS;

ACTIVATION FUNCTIONS; GENERALIZED COHEN-GROSSBERG NEURAL NETWORKS (GDCGNN); SYNAPTIC INTERCONNECTION WEIGHTS; TIME-VARYING DELAYS;

ASYMPTOTIC STABILITY;

EID: 33846390068     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.12.003     Document Type: Article

References (24)

1. Arik S. An analysis of global asymptotic stability of delayed cellular neural networks. IEEE Trans Neural Networks 13 5 (2002) 1239-1242
2. Arik S. An improved global stability result for delayed cellular neural networks. IEEE Trans Circuits Syst I 49 8 (2002) 1211-1214
3. Arik S. Global robust stability of delayed neural networks. IEEE Trans Circuits Syst I 50 1 (2003) 156-160
4. Chen T., and Amari S. Stability of asymmetric Hopfield networks. IEEE Trans Neural Networks 12 1 (2001) 159-163
5. Carpenter G.A. A geometric approach to singular perturbation problems with application to nerve impulse equation. J Differ Equat 23 3 (1977) 355-367
6. Cao J. A set of stability criteria for delayed cellular neural networks. IEEE Trans Circuits Syst I 48 11 (2001) 1330-1333
7. Cao J., and Wang J. Global asymptotic stability of a general class of recurrent neural networks with time-varying delays. IEEE Trans Circuits Syst I 50 1 (2003) 34-44
8. Cao J. New results concerning exponential stability and periodic solutions of delayed cellular neural networks. Phys Lett A 307 (2003) 136-147
9. Cohen M., and Grossberg S. Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybernet SMC-13 (1983) 815-826
10. Haykin S. Neural networks (1994), Prentice-Hall, NJ
11. Hastins A. Global stability in Lotka-Volterra system with diffusion. J Math Biol 6 (1978) 163-168
12. Hwang C., Cheng C., and Liao T. Globally exponential stability of generalized Cohen-Grossberg neural networks with delays. Phys Lett A 319 (2003) 157-166
13. Liang L., and Cao J. Global exponential stability of reaction-diffusion recurrent neural networks with time-varying delays. Phys Lett A 314 (2003) 434-442
14. Liao X., and Li J. Stability in Gilpin-Ayala competition models with diffusion. Nonlinear Anal 28 10 (1997) 1751-1758
15. Rothe F. Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. J Math Biol 3 (1976) 319-324
16. Sun J., and Wan L. Convergence dynamics of stochastic reaction-diffusion recurrent neural networks with delays. Int J Bifurc Chaos 15 7 (2005) 2131-2144
17. Sun J., and Wan L. Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays. Physica D 208 (2005) 1-20
18. Wan L., and Sun J. Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys Lett A 343 4 (2005) 306-318
19. Wan L., and Sun J. Global asymptotic stability of Cohen-Grossberg neural network with continuously distributed delays. Phys Lett A 343 4 (2005) 331-340
20. Wang L.S., and Xu D.Y. Global exponential stability of Hopfield reaction-diffusion neural networks with time-varying delays. Sci China (Ser F) 46 (2003) 466-474
21. Wang L.S., and Xu D.Y. Asymptotic behavior of a class of reaction-diffusion equations with delays. J Math Anal Appl 281 (2003) 439-453
22. Wang L., and Zou X.F. Exponential stability of Cohen-Grossberg neural networks. Neural Networks 15 (2002) 415-422
23. Wang L., and Zou X.F. Harmless delays in Cohen-Grossberg neural networks. Phys D 170 (2002) 162-173
24. Ye H., Michel A.N., and Wang K. Qualitative analysis of Cohen-Grossberg neural networks with multiple delays. Phys Rev E 51 (1995) 2611-2618