Exponential periodicity of continuous-time and discrete-time neural networks with delays

Neural Processing Letters

Volumn 19, Issue 2, 2004, Pages 131-146

  Sun, Changyin ^a,b   Feng, Chun Bo ^b  

^a HOHAI UNIVERSITY   (China)

^b SOUTHEAST UNIVERSITY   (China)

Author keywords

Activation functions; Delays; Discrete time analogue; Exponential periodicity; Exponential stability

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; FUNCTIONS; LEARNING ALGORITHMS; PROBLEM SOLVING; QUADRATIC PROGRAMMING; SYSTEM STABILITY; SYSTEMS ANALYSIS;

ACTIVATION FUNCTIONS; DELAYS; DISCRETE TIME ANALOG; EXPONENTIAL PERIODICITY; EXPONENTIAL STABILITY;

NEURAL NETWORKS;

EID: 3543071672     PISSN: 13704621     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NEPL.0000023421.60208.30     Document Type: Article

References (28)

1. Bouzerman, A. and Pattiaon, T.: Neural network for quadratic optimization with bound constraints. IEEE Trans. Neural Networks 4 (1993), 293-303.
2. Michel, A. N., Farrel, J. and Porod, W.: Qualitative analysis of neural networks. IEEE Trans. Circuits Systems I 37 (Oct. 1989), 229-243.
3. Cao, J.: On exponential stability and periodic solutions of CNNs with delays. Physics Letters A 267 (2000), 312-318.
4. Cao, J.: On exponential stability and periodic solutions of delayed celluler neural networks. Science in China 30(6) (2000), 541-549.
5. Liao, X. and Wang, J.: Algebraic criteria for global exponential stability of cellular neural networks with multiple time delays. IEEE Trans. Circuits Systems 150(2) (2003), 268-275.
6. Forti, M.: On global asymptotic stability of a class of nonlinear systems arising in neural network theory. Journal of differential equations 113 (1994), 246-264.
7. Forti, M. and Tesi, A.: New conditions for global stability of neural networks with application to linear and quadratic programming Problems. IEEE Trans. Circuits and Systems I 42 (1995), 354-366.
8. Venetianer, P. L. and Roska, T.: Image compression by delayed CNNs. IEEE Trans. Circuits Syst. I 45 (1998), 205-215.
9. Sudharsanan, S. and Sundareshan, M.: Exponential stability and a systematic synthesis of a neural network for quadratic minimization, Neural networks 4 (1991), 599-613.
10. Morita, M.: Associative memory with non-monntone dynamics. Neural networks 6 (1993), 115-126.
11. Tank, D. W. and Hopfield J. J.: Simple 'neural' optimization networks: An A/D converter, signal decision circuit, and a linear programming circuit, IEEE Trans. Circuits & Systems 33 (1986), 533-541.
12. Kennedy, M. and Chua, L.: Neural networks for linear and nonlinear programming. IEEE Trans. Circuits & Systems 35 (1988), 554-562.
13. Townley, S. et al.: Existence and learning of oscillations in recurrent neural networks. IEEE Trans. Neural Networks 11 (2000), 205-214.
14. Chen, Y. H. and Fang, S. C.: Neurocomputing with time delay analysis for solving convex quadratic programming problems. IEEE Trans. Neural Networks 11 (2000), 230-234.
15. Zhang, Y., Pheng, H. A. and Vadakkepat, P.: Absolute periodicity and absolute stability of delayed neural networks. IEEE Trans. Circuits and Systems: 149 (2002), 256-261.
16. Sun, C., Song, S. and Feng, C. B.: On global robust exponential stability of interval neural networks with delays, Proceedings of the 2002 International Joint Conference on Neural Networks. Hawaii, 3, 2738-2742, 2002.
17. Sun, C., Fei, S., Zhang, K., Cao, J. and Feng, C. B.: On absolute exponential stability of a class of neural networks, Proceedings of 15th International Federation of Automatic Contort (IFAC'02). Barcelona, Spain, July 21-26, 2002.
18. Sun, C. and Feng, C. B.: On exponential periodicity of delayed neural networks. In: Proceedings of the 2003 IEEE International Symposium on Circuits and Systems, May 25-28, pp. 681-684.
19. Sun, G. and Sun, C.: On absolute stability of delayed neural networks, Proceedings of The International Conference on Communication Circuits and Systems & West Sino-Expo 2002, pp. 1675-1679, 2002.
20. Sun, C. and Feng, C. B.: On exponential stability of delayed neural networks with globally lipschitz continuous activation functions. In: Proceedings of the 4th World Congress on Intelligent Control and Automation. Shanghai, Vol. 3, June 2002, pp. 1953-1957.
21. Sun, C., Zhang, K., Fei, S. and Feng, C. B.: On exponential stability of delayed neural networks with a general class of activation functions. Physics Letters A. 298(2/3) 2002, 122-132.
22. Sun, C. and Feng, C. B.: Global robust exponential stability of interval neural networks with delays. Neural Processing Letters 17(1) (2003), 107-115.
23. Sun, C., Liu, D. and Feng, C. B.: New results on exponential periodicity of delayed neural networks. In: Proceedings of the 2003 IEEE Joint Conference on Neural Networks (IJCNN'2003) pp. 902-907 Portland, Oregon, 2003.
24. Arik, S. and Tavsanoglu, V.: On the global asymptotic stability of delayed cellular neural networks. IEEE Trans. Circuits and Systems: 747(4) (2000), 571-574.
25. Gopalsamy, K. and He, X. Z.: Stability in asymmetric Hopfield nets with transmission delays. Physica D 76 (1994), 344-358.
26. Gopalsamy, K. and He, X. Z.: Delay-independent stability in bi-directional associative memory networks. IEEE Trans. Neural Networks 5 (1994), 998-1002.
27. Mohamad, S. and Gopalsamy, K.: Exponential stability of contiuous-time and discrete-time cellular neural networks with delays. Applied Mathematics and Computation 135 (2003), 17-38.
28. Mohamad, S.: Global exponential stability in continuous-time and discrete-time delay bi-directional neural networks. Physical D 159 (2001), 233-251.