Feedback anticontrol of discrete chaos

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 8, Issue 7, 1998, Pages 1585-1590

  Chen, Guanrong ^a   Lai, Dejian ^b  

^a University of Houston   (United States)

^b UNIVERSITY OF TEXAS SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039758367     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127498001236     Document Type: Article

References (28)

1. Brandt, M. E. & Chen, G. [1997] "Bifurcation control of two nonlinear models of cardiac activity," IEEE Trans. Circuits Syst. I 44, 1031-1034.
2. Chen, G. [1996] "Control and synchronization of chaotic systems (bibliography)," ECE Department University of Houston, TX 77204 - available by anonymous ftp: "ftp.egr.uh.edu/pub/TeX/chaos.tex"
3. Chen, G. & Dong, X. [1993a] "From chaos to order - Perspectives and methodologies in controlling chaotic nonlinear dynamical systems," Int. J. Bifurcation and Chaos 3, 1363-1410.
4. Chen, G. & Dong, X. [1993b] "Control of chaos - A survey," IEEE Conf. Decision and Control, San Antonio, TX, pp. 469-474.
5. Chen, G. & Dong, X. [1998] From Chaos to Order: Methodologies, Perspectives, and Applications (World Scientific, Singapore).
6. Chen, G. & Lai, D. [1996] "Feedback control of Lyapunov exponents for discrete-time dynamical systems," Int. J. Bifurcation and Chaos 6, 1341-1349.
7. Chen, G. & Lai, D. [1997a] "Making a dynamical system chaotic: Feedback control of Lyapunov exponents for discrete-time dynamical systems," IEEE Trans. Circuits Syst. I 44, 250-253 (see [1997b] for a correction).
8. Chen, G. & Lai, D. [1997b] "Anticontrol of chaos via feedback," Proc. IEEE Conf. Decison and Control, San Diego, CA, pp. 367-372.
9. Chen, G. & Moiola, J. L. [1994] "An overview of bifurcation, chaos and nonlinear dynamics in control systems," J. Franklin Institute 331B, 819-858.
10. Devaney, R. L. [1987] An Introduction to Chaotic Dynamical Systems (Addison-Wesley, NY).
11. Ditto, W. L. [1996] "Applications of chaos in biology and medicine," in Chaos and the Changing Nature of Science and Medicine: An Introduction, ed. Herbert, D. E. (AIP Press, NY), pp. 175-201.
12. Garfinkel, A., Spano, M. L., Ditto, W. L. & Weiss, J. N. [1992] "Controlling cardiac chaos," Science 257, 1230-1235.
13. Goldberger, A. L. [1994] "Applications of chaos to physiology and medicine," in Applied Chaos, eds. Kim, J. H. & Stringer, J. (Academic Press, NY), pp. 321-331.
14. Holzfuss, J. & Parlitz, U. [1991] "Lyapunov exponents from time series," in Lyapunov Exponents, eds. Arnold, L., Crauel, H. & Eckmann, J.-P. (Springer-Verlag, NY), pp. 263-270.
15. In, V., Mahan, S. E., Ditto, W. L. & Spano, M. L. [1995] "Experimental maintenance of chaos," Phys. Rev. Lett. 74, 4420-4423.
16. Kapitaniak, T. [1996] Controlling Chaos: Theoretical and Practical Methods in Nonlinear Dynamics (Academic Press, London).
17. Lakshmanan, M. & Murali, K. [1996] Chaos in Nonlinear Oscillators: Controlling and Synchronization (World Scientific, Singapore).
18. Ogorzalek, M. J. [1993] "Taming chaos, Part II: Control," IEEE Trans. Circuits Syst. I 40, 700-706.
19. Ogorzalek, M. J. [1994] "Chaos control: How to avoid chaos or take advantage of it," J. Franklin Institute 331B, 681-704.
20. Rao, C. R. [1973] Linear Statistical Inference and Its Applications, 2nd edition (Wiley, NY).
21. Oseledec, V. I. [1968] "A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems," Trans. Moscow Math. Soc. 19, 197-231.
22. Schiff, S. J., Jerger, K., Duong, D. H., Chang, T., Spano, M. L. & Ditto, W. L. [1994] "Controlling chaos in the brain," Nature 370, 615-620.
23. Shinbrot, T., Grebogi, C., Ott, E. & Yorke, J. A. [1993] "Using small perturbations to control chaos," Nature 363, 411-417.
24. Skarda, C. A. & Freeman, W. J. [1987] "How brain make chaos in order to make sense to the world," Behav. Brain Sci. 10, 161-195.
25. Touhey, P. [1997] "Yet another definition of chaos," Amer. Math. Monthly, May 1997, 411-414.
26. Tsuda, I. & Barna, G. [1994] "How can chaos be a cognitive processor?" in Towards the Harnessing of Chaos, ed. Yamaguti, M. (Elsevier Science, NY), pp. 47-61.
27. Wiggins, S. [1990] Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, NY).
28. Yang, W., Ding, M., Mandell, A. J. & Ott, E. [1995] "Preserving chaos: Control strategies to preserve complex dynamics with potential relevance to biological disorders," Phys. Rev. E51, 102-110.