Chaotification via arbitrarily small feedback controls: Theory, method, and applications

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 10, Issue 3, 2000, Pages 549-570

  Wang, Xiao Fan ^a   Chen, Guanrong ^b  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF HOUSTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039772222     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127400000372     Document Type: Article

References (37)

1. Bollt, E. M. [1999] "Stability of order: An example of horseshoes 'near' a linear map," Int. J. Bifurcation and Chaos 9(10), 2081-2090.
2. Brandt, M. E. & Chen, G. [1997] "Bifurcation control of two nonlinear models of cardiac activity," IEEE Trans. Circuits Syst. I 44, 1031-1034.
3. Chen, G. (ed.) [1999] Controlling Chaos and Bifurcations in Engineering Systems (CRC Press, Boca Raton, FL).
4. Chen, G. & Dong, X. [1998] From Chaos to Order: Methodologies, Perspectives, and Applications (World Scientific, Singapore).
5. Chen, G., Hsu, S. B. & Zhou, J. [1998] "Snapback repeller as a cause of chaotic vibration of the wave equation with a van der Pol boundary condition and energy injection at the middle of the span," J. Math. Phys. 39, 6459-6489.
6. Chen, M., Chen, Z. & Chen, G. [1997] Approximate Solutions of Operator Equations (World Scientific, Singapore).
7. Chen, G. & Lai, D. [1996] "Feedback control of Lyapunov exponents for discrete-time dynamical systems," Int. J. Bifurcation and Chaos 6, 1341-1349.
8. Chen, G. & Lai, D. [1997] "Anticontrol of chaos via feedback," Proc. IEEE Conf. Decision and Control, San Diego, CA, Dec. 10-12, 1997, pp. 367-372.
9. Chen, G. & Lai, D. [1998] "Feedback anticontrol of discrete chaos," Int. J. Bifurcation and Chaos 8, 1585-1590.
10. Chen, L. & Aihara, K. [1997] "Chaos and asymptotical stability in discrete-time neural networks," Physica, D104, 286-325.
11. Devaney, R. L. [1987] An Introduction to Chaotic Dynamical Systems (Addison-Wesley, NY).
12. 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.
13. Fang, J.-Q. & Ali, M. K. [1999] "Control and synchronization of spatiotemporal chaos," Controlling Chaos and Bifurcations in Engineering Systems, ed. Chen, G. (CRC Press: Bota Raton, FL), pp. 104-127.
14. Fradkov, A. L. & Pogromsky, A. Yu. [1999] Introduction to Control of Oscillations and Chaos (World Scientific, Singapore).
15. Freeman, W. J. [1995] "Chaos in the brain: Possible roles in biological intelligence," Int. J. Intell. Syst. 10, 71-88.
16. Garfinkel, A., Spano, M. L., Ditto, W. L. & Weiss, J. N. [1992] "Controlling cardiac chaos," Science 257, 1230-1235.
17. Golub, G. H. & Van Loan, C. F. [1983] Matrix Computations (Johns Hopkins University Press).
18. In, V., Mahan, S. E., Ditto, W. L. & Spano, M. L. [1995] "Experimental maintenance of chaos," Phys. Rev. Lett. 74, 4420-4423.
19. Judd, K., Mees, A., Teo, K. L. & Vincent, T. (eds.) [1997] Control and Chaos: Mathematical Modeling (Birkhauser, Boston).
20. Kapitaniak, T. [1998] Chaos for Engineers: Theory, Applications, and Control (Springer-Verlag, NY).
21. Khalil, H. K. [1996] Nonlinear Systems, 2nd edition (Macmillan, NY).
22. Kostelich, E. J. & Barreto, E. [1997] "Targeting and control of chaos," in Control and Chaos, eds. Judd, K., Mees, A., Teo, K. L. & Vincent, T. L. (Birkhauser, Boston), pp. 158-169.
23. Lakshmanan, M. & Murali, K. [1996] Chaos in Nonlinear Oscillators: Controlling and Synchronization (World Scientific, Singapore).
24. Li, T. Y. & Yorke, J. A. [1975] "Period three implies chaos," Amer. Math. Monthly 82, 481-485.
25. n," J. Math. Anal. Appl. 63, 199-223.
26. 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.
27. Shinbrot, T., Grebogi, C., Ott, E. & Yorke, J. A. [1993] "Using small perturbations to control chaos," Nature 363, 411-417.
28. Shiraiwa, K. & Kurata, M. [1980] "A generalization of a theorem of Marotto," Proc. Japan Acad. 55, 286-289.
29. 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.
30. Smale, S. [1968] "Diffeomorphisms with many periodic points," in Differential and Combinatorial Topology (Princeton Univ. Press, Princeton, NJ), pp. 63-80.
31. Suykens, A. K., Vandewalle, J. & De Moor, B. L. R. [1996] ANNs for Modelling and Control of Nonlinear Systems (Kluwer Academic Pub., Netherlands).
32. Ushio, T. & Hirai, K. [1983] "Chaos in nonlinear sampled-data control systems," Int. J. Control 38, 1023-1033.
33. Ushio, T. & Hirai, K. [1985] "Chaotic behavior in piecewise-linear sampled-data control systems," Int. J. Nonlin. Mech. 20, 493-506.
34. Vanecek, A. & S. Celikovsky [1996] Control Systems: From Linear Analysis to Synthesis of Chaos (Prentice-Hall, London).
35. Vincent, T. L. [1997] "Control using chaos," IEEE Control Syst. Mag., December, 65-76.
36. Wang, X. F. & Chen, G. [2000] "Chaotifying a stable LTI system by tiny feedback control," IEEE Trans. Circuits Syst., in press.
37. 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.