Periodic solution and global exponential stability for shunting inhibitory delayed cellular neural networks

Electronic Journal of Differential Equations

Volumn 2004, Issue , 2004, Pages

  Chen, Anping ^a   Cao, Jinde ^b   Huang, Lihong ^c  

^a XIANGNAN UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

^c HUNAN UNIVERSITY   (China)

Author keywords

Global exponential stability; Lyapunov functionals; Periodic solutions; Poincar mapping; Shunting inhibitory delay cellular neural networks

Indexed keywords

EID: 9344245669     PISSN: 10726691     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (40)

1. S. Arik, V. Tavsanoglu, Equilibrium analysis of delayed CNNs. IEEE Trans. Circuits Syst.-I, vol. 45, no. 2, pp. 168-171, 1998.
2. S. Arik, An improned global stability results for delayed cellular neural networks, IEEE Trans. Circuits Syst.-I, vol. 49, no. 8, pp. 1211-1214, 2002.
3. A. Bouzerdoum, R. B. Pinter, A shunting inhibitory motion detector that can account for the functional characteristics of fly motionsensitive interneurons, in: Proceedings of International Joint Conference Neural Networks, 1990.
4. A. Bouzerdoum, R. B. Pinter, Analysis and analog implementation of directionally sensitive shunting inhibitory cellular neural networks, in: Visual Information Processing: From Neurons to Chips, vol. SPIE-1473, pp. 29-38, 1991.
5. A. Bouzerdoum, R. B. Pinter, Nonlinear lateral inhibition applied to motion detection in the fly visual system, in R. B. Pinter, B. Nabet(Eds.), Nonlinear Vision, CRC Press, Boca Raton, FL, pp. 423-450, 1992.
6. A. Bouzerdoum, R. B. Pinter, Shunting inhibitory cellular networks: derivarion and stability analysis, IEEE Trans. Circuits Syst.-I vol. 40, pp. 215-218, 1993.
7. J. Cao, Periodic solutions and exponential stability in delayed cellular neural networks, Physical Review E, vol. 60, no. 3, pp. 3244-3248, 1999.
8. J. Cao and D. Zhou, Stability analysis of delayed cellular neural networks. Neural Networks, vol. 11, no. 9, pp. 1601-1605, 1998.
9. J. Cao, L. Wang. Periodic oscillatory solution of bidirectional associative memory networks with delays, Physical Review E, vol. 61, no. 2, pp. 1825-1828, 2000.
10. J. Cao, Global exponential stability and periodic solutions of delayed cellular neural networks, Journal of Computer and System Sciences, vol. 60, no. 1, pp. 38-46, 2000.
11. J. Cao, Global exponential stability and periodic solutions of CNNs with delays, Physics Letters A, vol. 267, pp. 312-318, 2000.
12. J. Cao, Exponential stability and periodic solutions of delayed cellular neural networks, Science in China (Series E), vol. 43, no. 3, pp. 328-336, 2000.
13. A. Chen and J. Cao, Almost periodic solution of shunting inhibitory CNNs with delays, Physics Letters A, vol. 298, pp. 161-170, 2002.
14. A. Chen, L. Huang, J. Cao, Existence and stability of almost periodic solution for BAM neural networks with delays, Appl. Math. Comput., vol. 137, pp. 177-193, 2003.
15. A. Chen, J. Cao, Existence and attractivity of almost periodic solution for cellular neural networks with distributed delays and variable coefficients, Appl. Math. Comput., vol. 135, pp. 125-140, 2003.
16. A. Chen, J. Cao, and L. Huang, An Estimation of Upperbound of Delays for Global Asymptotic Stability of Delayed Hopfield Neural Networks, IEEE Trans. on Circuits and Syst.-I, vol. 49, No. 7, pp. 1028-1032, 2002.
17. L. O. Chua and L. Yang, Cellular neural networks: Theory. IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1257-1272, 1988.
18. L. O. Chua and L. Yang, Cellular neural networks: Applications. IEEE Trans. Circuits Syst., vol. 35, no. 10, pp. 1273-1290, 1988.
19. P. V. D. Driessche and X. Zou, Global attractivity in delayed Hopfield neural networks models, SIAM, J. Appl. Math., vol. 58, no. 6, pp. 1878-1890, 1998.
20. P. P. Civalleri and M. Gilli, On stability of cellular neural networks with delay. IEEE Trans. Circuits Syst.-I, vol. 40, no. 3, pp. 157-165, 1993.
21. M. Forti, Some extension of a new method to analyze complete stability of neural networks, IEEE Trans. Neural Networks, vol. 13, no. 5, pp. 1230-1238, 2002.
22. M. Gilli, Stability of cellular neural networks and delayed cellular neural networks with nonposive templates and nonmonotonic output functions. IEEE Trans. Circuits Syst.-I, vol. 41, pp. 518-528, 1994.
23. K. Gopalsamy and X. Z. He, Delay-independent stability in bi-directional associative memory networks, IEEE Trans. Neural Networks, vol. 5, no.6, 998-1002, 1994.
24. M. E. Jernigen, G. F. Mclean, Lateral inhibition and image processing, in: R.B. Pinter, B. Nabet(Eds.), Nonlinear Vision, CRC Press, Boca Raton, FL, 1992.
25. M. E. Jenigen, R. J. Belshaw, G. F. Mclean, Nonlinear lateral inhibition and image processing, in: B. Nabet, R.B. Pinter(Eds.), Sensory Neural Networks: Lateral Inhibition, CRC Press, Boca Raton, FL, pp. 27-45, 1991.
26. X. X. Liao, Stability of the Hopfield neural networks, Science in China, vol. 23, no.5, pp. 523-532, 1993.
27. X. B. Liang, Global exponential stability and application of the Hopfield neural networks, Science in China, vol. 25, no. 5, pp. 523-532, 1995.
28. K. Mastsuoka, Stability conditions for nonlinear continuous neural networks with asymmetric connection weight, Neural Networks, vol. 5, pp. 495-500, 1992
29. R. B. Pinter, R. M. Olberg, E. Warrant, Luminance adaption of preferred object size in identified dragonfly movement detectors, in: Proceedings of IEEE International Conference SMC, 1989, pp. 682-686.
30. T. Roska and T. Boros, P. Thiran, L. O. Chua, Detecting si,ple motion using cellular neural networks, in: proceedings of IEEE International Workshop on Cellular Neural Networks and Their Applications, 1990, pp. 127-138.
31. T. Roska and L. O. Chua, Cellular neural networks with nonlinear and delay-type template. Int. J. Circuit Theory Appl., vol. 20, pp. 469-481, 1992.
32. T. Roska, C.W. Wu and L. O. Chua, Stability of cellular neural networks with dominant nonlinear and delay-type template. IEEE Trans. Circuits Syst.-I, vol. 40, no. 4, pp. 270-272, 1993.
33. T. Roska, C.W. Wu, M. Balsi and L. O. Chua, Stability and dynamics of delay-type general and cellular neural networks. IEEE Trans. Circuits Syst.-I, vol. 39, no. 6, pp. 487-490, 1992.
34. F. Zou, S. Schwartz, J. Nossek, Cellular neural networks design using a learning algorithm, in: Proceedings of IEEE International Workshop on Cellular Neural Networks and Their Applications, pp. 73-81, 1990.
35. J. Y. Zhang, X. S. Jin, Global stability analysis in delayed Hopfield neural network models, IEEE Trans. Neural Networks, vol. 13, pp. 745-753, 2000.
36. H. Huang, J. Cao, J. Wang, Global exponential stability and periodic solutions of recurrent neural networks with delays, Physics Letters A, vol. 298, nos.5-6, pp. 393-404, 2002.
37. J. Cao, New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Physics Letters A, vol. 307, nos. 2-3, pp. 144-155, 2003.
38. J. Cao, J. Wang, Global asymptotic stability of a general class of recurrent neural networks with time-varying delays, IEEE Trans. Circuits Syst.-I, vol. 50, no. 1, pp. 34-44, 2003.
39. J. Cao, J. Wang, X. Liao, Novel stability criteria of delayed cellular neural networks, Inter. J. Neural Syst., vol. 13, no. 5, pp. 367-375, 2003.
40. X. Huang, J. Cao, Almost periodic solution of shunting inhibitory cellular neural networks with time-varying delays, Physics Letters A, vol. 314, no. 3, pp. 222-231, 2003.