Exponential stability of stochastic delayed Hopfield neural networks

Applied Mathematics and Computation

Volumn 199, Issue 1, 2008, Pages 84-89

  Zhou, Qinghua ^a   Wan, Li ^b  

^a ZHAOQING UNIVERSITY   (China)

^b WUHAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Delay; Exponential stability; Hopfield neural networks

Indexed keywords

ASYMPTOTIC STABILITY; NUMERICAL METHODS; PROBLEM SOLVING; STOCHASTIC MODELS;

DELAY; EQUILIBRIUM SOLUTION; MEAN SQUARE; STOCHASTIC DELAY;

HOPFIELD NEURAL NETWORKS;

EID: 41949092085     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.09.025     Document Type: Article

References (29)

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. Circ. Syst. I 49 8 (2002) 1211-1214
3. Arik S. Global robust stability of delayed neural networks. IEEE Trans. Circ. Syst. I 50 1 (2003) 156-160
4. Blythe S., Mao X., and Liao X. Stability of stochastic delay neural networks. J. Franklin Inst. 338 (2001) 481-495
5. Buhmann J., and Schulten K. Influence of noise on the function of a 'physiological' neural network. Biol. Cynern. 56 (1987) 313-327
6. Cao J. A set of stability criteria for delayed cellular neural networks. IEEE Trans. Circ. 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. Circ. 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. Chen T., and Amari S. Stability of asymmetric Hopfield networks. IEEE Trans. Neural Networks 12 1 (2001) 159-163
10. Chen T., and Amari S. New theorems on global convergence of some dynamical systems. Neural Networks 14 3 (2001) 251-255
11. Chua L.O., and Yang L. Cellular neural networks: applications. IEEE Trans. Circ. Syst. 35 10 (1988) 1273-1290
12. Chua L.O., and Yang L. Cellular neural networks: theory. IEEE Trans. Circ. Syst. 35 10 (1988) 1257-1272
13. Chua L.O., and Roska T. The CNN paradigm. IEEE Trans. Circ. Syst. I 40 3 (1993) 147-156
14. Le Cun Y., Galland C.C., and Hinton G.E. GEMINI: gradient estimation through matrix inversion after noise injection. In: Touretzky D.S. (Ed). Advances in Neural Information Processing Systems vol. 1 (1989), Morgan Kaufmann, San Mateo 141-148
15. Haykin S. Neural Networks (1994), Prentice-Hall, NJ
16. Hopfield J.J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79 (1982) 2554-2558
17. Hopfield J.J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA 81 (1984) 3088-3092
18. Hopfield J.J., and Tank D.W. Computing with neural circuits: a model. Science 233 (1986) 625-633
19. Liao X., and Mao X. Exponential stability and instability of stochastic neural networks. Stochast. Anal. Appl. 14 2 (1996) 165-185
20. Liao X., and Mao X. Stability of stochastic neural networks. Neural, Parallel Sci. Comput. 4 2 (1996) 205-224
21. Mao X. Stochastic Differential Equations and Applications (1997), Horwood Publishing
22. Sun J., and Wan L. Convergence dynamics of stochastic reaction-diffusion recurrent neural networks with delays. Int. J. Bifurcat. Chaos 15 7 (2005) 2131-2144
23. 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
24. Wan L., and Sun J. Mean square exponential stability of stochastic delayed Hopfield neural networks. Phys. Lett. A 343 (2005) 306-318
25. Wan L., and Sun J. Global asymptotic stability of Cohen-Grossberg neural network with continuously distributed delays. Phys. Lett. A 342 (2005) 331-340
26. Zhang J., and Jin X. Global stability analysis in delayed Hopfield neural network models. Neural Networks 13 (2000) 745-753
27. Zhou Q., Sun J., and Chen G. Global exponential stability and periodic oscillations of reaction-diffusion BAM neural networks with periodic coefficients and general delays. Int. J. Bifurcat. Chaos 17 (2007) 129-142
28. Zhou Q., Wan L., and Sun J. Exponential stability of reaction-diffusion generalized Cohen-Grossberg neural networks with time-varying delays. Chaos Soliton. Fract. 32 (2007) 1713-1719
29. Zhang Q., Wei X., and Xu J. Global exponential stability of Hopfield neural networks with continuously distributed delays. Phys. Lett. A 315 (2003) 431-436