Global exponential stability in Hopfield and bidirectional associative memory neural networks with time delays

Chinese Annals of Mathematics. Series B

Volumn 25, Issue 2, 2004, Pages 255-262

  Rong, Libin ^a   Lu, Wenlian ^a   Chen, Tianping ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Bidirectional associative memory (BAM); Global exponential stability; Hopfield neural network; Lyapunov functional; Time delays

Indexed keywords

EID: 4444319835     PISSN: 02529599     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0252959904000263     Document Type: Article

References (25)

1. Hopfield, J. J., Neurons with graded response have collective computational properties like those of two-stage neurons, Proc. Nat. Acad. Sci. USA, 81(1984), 3088-3092.
2. Marcus, C. M. & Westervelt, R. M., Stability of analog neural networks with delay, Phys. Rev. A, 39(1989), 347-359.
3. Gopalsamy, K. & He, X., Stability in asymmetric Hopfield nets with transmission delays, Phys. D, 76(1994), 344-358.
4. Zhang, J. & Jin, X., Global stability analysis in delayed Hopfield neural network models, Neural Networks, 13(2000), 745-753.
5. Cao, Y. & Wu, Q., A note on stability of analog neural networks with time delays, IEEE Trans. Neural Networks, 7(1996), 1533-1535.
6. Cao, J., On exponentical stability and periodic solutions of CNNs with delays, Phys. Lett. A, 267:5-6(2000), 312-318.
7. Cao, J. & Li, Q., On the exponentical stability and periodic solutions of delayed cellular neural networks, J. Math. Analysis and Appl., 252(2000), 50-64.
8. Cao, J., Global exponential stability of Hopfield neural networks, Int. J. Syst. Sci., 32:2(2001), 233-236.
9. Cao, J., Global stability conditions for delayed CNNs, IEEE Trans. CAS, 48:11(2001), 1330-1333.
10. Driessche, P. V. & Zou, X., Global attractivity in delayed Hopfield neural network models, SIAM J. Appl. Math., 58:6(1998), 1878-1890.
11. Driessche, P. V., Wu, J. & Zou, X., Stabilization role of inhibitory self-connections in a delayed neural network, Phys. D, 150(2001), 84-90.
12. Chu, T., An exponential convergence estimate for analog neural networks with delay, Phys. Lett. A, 283(2001), 113-118.
13. Peng, J., Qiao, H. & Xu, Z., A new approach to stability of neural networks with time-varying delays, Neural Networks, 15(2002), 95-103.
14. Chen, T. P. & Amari, S., Exponential convergence of delayed dynamical systems, Neural Computation, 13:3(2001), 621-636.
15. Chen, T. P., Convergence of delayed dynamical systems, Neural Processing Letters, 10:3(1999), 267-271.
16. Arik, S. & Tavsanoglu, V., On the global asymptotic stability of delayed cellular neural networks, IEEE Trans. Circuits Syst. I, 47:4(2000), 571-574.
17. Liao, T. & Wang, F., Global stability for cellular neural networks with time delay, IEEE Trans. Neural Networks, 11:6(2000), 1481-1484.
18. Kosko, B., Adaptive bidirectional associative memories, Appl. Opt., 26(1987), 4947-4960.
19. Kosko, B., Bidirectional associative memories, IEEE Trans. Syst. Man Cybernet, 18(1988), 49-60.
20. Kosko, B., Unsupervised learning in noise, IEEE Trans. Neural Networks, 1(1990), 44-57.
21. Liao, X. & YU, J., Qualitative analysis of bi-directional associative memory with time delay, Int. J. Circ. Theor. Appl, 26(1998), 219-229.
22. Gopalsamy, K. & He, X., Delay-independent stability in bidirectional associative memory networks, IEEE Trans. Neural Networks, 5:6(1994), 998-1002.
23. Mohamad, S., Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks, Phys. D, 159(2001), 233-251.
24. Sree Hari Rao, V. & Phaneendra, B., Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones, Neural Networks, 12(1999), 455-465.
25. Joy, M., Results concerning the absolute stability of delayed neural networks, Neural Networks, 13(2000), 613-616.