Chaotifying linear Elman networks

IEEE Transactions on Neural Networks

Volumn 13, Issue 5, 2002, Pages 1193-1199

  Li, Xiang ^a,b   Chen, Guanrong ^b   Chen, Zengqiang ^a   Yuan, Zhuzhi ^a  

^a NANKAI UNIVERSITY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Chaos generation; Chaotification; Li Yorke chaos; Linear Elman network

Indexed keywords

ADAPTIVE CONTROL SYSTEMS; CHAOS THEORY; COMPUTER SIMULATION; LINEAR CONTROL SYSTEMS;

LINEAR ELMAN NETWORKS;

RECURRENT NEURAL NETWORKS;

EID: 0036738826     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2002.1031950     Document Type: Article

References (24)

1. W. J. Freeman, "The physiology of perception", Sci. Amer., pp. 78-85, Feb. 1991.
2. C.M. Marcus and R. M. Westervelt, "Dynamics of iterated-map neural networks", Phys. Rev. A, vol. 40, pp. 501-504, 1989.
3. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications. Singapore: World Scientific, 1998.
4. K. Aihara, T. Takabe, and M. Toyoda, "Chaotic neural networks", Phys. Lett. A, vol. 144, pp. 333-340, 1990.
5. L. Chen and K. Aihara, "Chaos and asymptotical stability in discrete-time neural networks", Phys. D, vol. 104, pp. 286-325, 1997.
6. X.F. Wang and G. Chen, "Chaotification via arbitrarily small feedback controls: Theory, method and applications", Int. J. Bifurcation Chaos, vol. 10, pp. 549-570, 2000.
7. X. Li, Z. Chen, Z. Yuan, and G. Chen, "Generating chaos by an Elman network", IEEE Trans. Circuits Syst. I, vol. 48, pp. 1126-1131, 2001.
8. J. L. Elman, "Finding structure in time", Cogn. Sci., vol. 14, pp. 179-211, 1990.
9. F. R. Marotto, "Snap-back repellers imply chaos", J. Math. Anal. Applicat., vol. 63, pp. 199-223, 1978.
10. T. Y. Li and J. A. Yorke, "Period three implies chaos", Amer. Math. Monthly, vol. 82, pp. 481-485, 1975.
11. G. H. Golub and C. F. van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1983.
12. D.T. Pham and X. Liu, "Training of Elman network and dynamic system modeling", Int. J. Syst. Sci., vol. 27, pp. 221-226, 1996.
13. A. Sperduti, "On the computational power of recurrent neural networks for structures", Neural Networks, vol. 10, pp. 395-400, 1997.
14. X. Li, Z. Chen, and Z. Yuan, "Nonlinear stable adaptive control based upon Elman networks", Appl. Math. J. Chinese Univ.: Ser. B, vol. 15, pp. 332-340, 2000.
15. _, "Simple recurrent neural networks control for nonminimum phase nonlinear systems", Chin. J. Contr. Theory Applicat., vol. 18, pp. 456-460, 2001.
16. D.R. Frey, "Chaotic digital encoding: An approach to secure communication", IEEE Trans. Circuits Syst. II, vol. 40, pp. 660-666, 1993.
17. M. Goetz, K. Kelber, and W. Schwartz, "Discrete-time chaotic encryption systems-Part I: Statistical design approach", IEEE Trans. Circuits Syst. I, vol. 44, pp. 963-970, 1997.
18. S. Ishii, K. Fukumizu, and S. Watanabe, "A network of chaotic elements for information processing", Neural Networks, vol. 7, pp. 25-40, 1996.
19. _, "Associative memory based on parametrically coupled chaotic elements", Phys. D, vol. 121, pp. 344-366, 1998.
20. I. Tsuda, "Dynamic link of memory, Chaotic memory map in nonequilibrium neural networks", Neural Networks, vol. 5, pp. 313-326, 1992.
21. L. Chen and K. Aihara, "Chaotic simulated annealing by a neural network model with transient chaos", Neural Networks, vol. 8, pp. 915-930, 1995.
22. _, "Global searching ability of chaotic neural networks", IEEE Trans. Circuits Syst. I, vol. 46, pp. 974-993, 1999.
23. X. Li, Z. Chen, and Z. Yuan, "Simple recurrent neural networks-based adaptive predictive control for nonlinear systems", Asian J. Contr., 2002. to be published.
24. M. Hasegawa, T. Ikeguchi, and K. Aihara, "Solving large scale traveling salesman problems by chaotic neurodynamics", Neural Networks, vol. 15, pp. 271-283, 2002.