Anticontrol of chaos in continuous-time systems via time-delay feedback

Chaos

Volumn 10, Issue 4, 2000, Pages 771-779

  Wang, Xiao Fan ^a   Chen, Guanrong ^b,c   Yu, Xinghuo ^d  

^a NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF HOUSTON   (United States)

^c CITY UNIVERSITY OF HONG KONG   (Hong Kong)

^d CENTRAL QUEENSLAND UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034366942     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1322358     Document Type: Article

References (30)

1. Controlling Chaos and Bifurcations in Engineering Systems, edited by G. Chen (CRC, Boca Raton, FL, 1999).
2. G. Chen and X. Dong, From Chaos 10 Order: Perspectives, Methodologies, and Applications (World Scientific, Singapore, 1998).
3. A. L. Fradkov and A. Yu. Pogromsky, Introduction to Control of Oscillations and Chaos (World Scientific, Singapore, 1999).
4. Control and Chaos: Mathematical Modeling edited by K. Judd, A. Mees, K. L. Teo, and T. Vincent (Birkhauser, Boston, 1997).
5. T. Kapitaniak, Chaos for Engineers: Theory, Applications, and Control (Springer, New York, 1998).
6. M. Lakshmanan and K. Murali, Chaos in Nonlinear Oscillators: Controlling and Synchronization (World Scientific. Singapore, 1996).
7. J. M. Ottino et al., "Chaos, symmetry, and self-similarity: Exploiting order and disorder in mixing processes," Science 257, 754-760 (1992).
8. S. J. Schiff, K. Jerger, D. H. Duong, T. Chang, M. L. Spano, and W. L. Ditto, "Controlling chaos in the brain," Nature (London) 370, 615-620 (1994).
9. M. E. Brandt and G. Chen, "Bifurcation control of two nonlinear models of cardiac activity," IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 44, 1031-1034 (1997).
10. I. T. Georgiou and I. B. Schwartz, "Dynamics of large scale coupled structural/mechanical systems: A singular perturbation/proper orthogonal decomposition approach," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 59, 1178-1207 (1999).
11. M. P. Kennedy, G. Kolumban, and G. Kis, "Chaotic modulation for robust digital communications over multipath channels," Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 695-718 (2000).
12. M. Hasler and T. Schimming, "Chaos communication over noisy channels," Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 719-732 (2000).
13. E. M. Bollt, "Stability of order: An example of horseshoes 'near' a linear map," Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 2081-2090 (1999).
14. G. Chen and D. Lai, "Feedback control of Lyapunov exponents for discrete-time dynamical systems," Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, 1341-1349 (1996).
15. G. Chen and D. Lai, "Feedback anticontrol of discrete chaos," Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 1585-1590 (1998).
16. A. Vanecek and S. Celikovsky, Control Systems: From Linear Analysis to Synthesis of Chaos (Prentice-Hall, London, 1996).
17. X. F. Wang and G. Chen, "On feedback anticontrol of discrete chaos," Int. J. Bifurcation Chaos Appl. Sci. Eng. 9, 1435-1442 (1999).
18. X. F. Wang and G. Chen, "Chaotifying a stable LTI system by tiny feedback control," IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 47, 410-415 (2000).
19. X. F. Wang and G. Chen, "Chaotilication via arbitrarily small feedback controls: Theory, method and applications," Int. J. Bifurcation Chaos Appl. Sci. Eng. 10, 549-570 (2000).
20. E. Ott, C. Grebogi, and J. A. Yorke, "Controlling chaos," Phys. Rev. Lett. 64, 1196-1199 (1990).
21. M. C. Mackey and L. Glass, "Oscillation and chaos in physiological control systems," Science 197, 287-289 (1977).
22. J. D. Farmer, "Chaotic attractors of an infinite-dimensional dynamical systems," Physica D 4, 366-393 (1982).
23. K. Ikeda and K. Matsumoto, "High-dimensional chaotic behavior in systems with time-delay feedback," Physica D 29, 223-235 (1987).
24. O. Diekmann, S. A. van Gils, S. M. verduyn Lunel, and H.-O. Walther, Delay Equations: Functional-, Complex-, and Nonlinear Analysis (Springer, Berlin, 1995).
25. H. Lu and Z. He, "Chaotic behaviors in first-order autonomous continuous-time systems with delay," IEEE Trans. Circuits Syst. Video Technol. 43, 700-702 (1996).
26. P. Celka, "Delay-differential equations versus ID-map: Application to chaos control," Physica D 104, 127-147 (1997).
27. T. Y. Li and J. A. Yorke, "Period three implies chaos," Am. Math. Monthly 82, 481-485 (1975).
28. T. Kailath, Linear Systems (Prentice-Hall, Englewood Cliffs, NJ, 1980).
29. A. Isidori, Nonlinear Control Systems (Springer, Berlin, 1995).
30. L. O. Chua, C. W. Wu, A. Huang, and G.-Q. Zhong, "A universal circuit for studying and generating chaos. I. Routes to chaos," IEEE Trans. Circuits Syst. Video Technol. 40, 732-742 (1993).