Persistence of chaos in a time-delayed-feedback controlled Duffing system

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 3, 2006, Pages

  Yamasue, Kohei ^a   Hikihara, Takashi ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROLLED DUFFING SYSTEM; GLOBAL CHAOTIC DYNAMICS; TWO-WELL DUFFING SYSTEM;

CONVERGENCE OF NUMERICAL METHODS; DYNAMICS; FEEDBACK CONTROL; ORBITS;

CHAOS THEORY;

EID: 33645002452     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.036209     Document Type: Article

References (31)

1. Handbook of Chaos Control, edited by, H. G. Schuster, (Wiley-VCH, Weinheim, 1999).
2. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.64.1196 64, 1196 (1990).
3. K. Pyragas, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(92)90745-8 170, 421 (1992).
4. K. Pyragas and A. Tamaševičius, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(93)90501-P 180, 99 (1993).
5. J. E. S. Socolar, D. W. Sukow, and D. J. Gauthier, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.50.3245 50, 3245 (1994).
6. S. Bielawski, D. Derozier, and P. Glorieux, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.49.R971 49, R971 (1994).
7. T. Pierre, G. Bonhomme, and A. Atipo, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.76.2290 76, 2290 (1996).
8. T. Hikihara and T. Kawagoshi, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(95)00925-6 211, 29 (1996).
9. P. Parmananda, R. Madrigal, M. Rivera, L. Nyikos, I. Z. Kiss, and V. Gáspár, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.59.5266 59, 5266 (1999).
10. K. Pyragas, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(95)00654-L 206, 323 (1995).
11. H. Nakajima, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(97)00362-9 232, 207 (1997).
12. W. Just, T. Bernard, M. Ostheimer, E. Reibold, and H. Benner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.203 78, 203 (1997).
13. H. Nakajima and Y. Ueda, Physica D PDNPDT 0167-2789 10.1016/S0167- 2789(97)80009-7 111, 143 (1998).
14. W. Just, E. Reibold, K. Kacperski, P. Fronczak, J. A. Holyst, and H. Benner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.5045 61, 5045 (2000).
15. K. Pyragas, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.86.2265 86, 2265 (2001).
16. P. Hövel and J. E. S. Socolar, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.036206 68, 036206 (2003).
17. T. Ushio, IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. ITCAEX 1057-7122 10.1109/81.536757 43, 815 (1996).
18. T. Hikihara and Y. Ueda, Chaos CHAOEH 1054-1500 10.1063/1.166461 9, 887 (1999).
19. J. K. Hale, Theory of Functional Differential Equations (Springer-Verlag, New York, 1977).
20. K. Yamasue and T. Hikihara, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.056209 69, 056209 (2004).
21. F. C. Moon and P. J. Holmes, J. Sound Vib. JSVIAG 0022-460X 10.1016/0022-460X(79)90520-0 65, 275 (1979).
22. G. Duffing, Erwungene Schwingungen bei Veränderlicher Eigenfrequenz und Ihre Technische Bedeutung (Druck und Verlag von Friedr. Vieweg & Sohn, Braunschweig, 1918).
23. Y. Ueda, H. Nakajima, T. Hikihara, and H. B. Stewart, in Dynamical Systems Approaches to Nonlinear Problems in Systems and Circuits, edited by, F. M. A. Salam, and, M. L. Levi, (SIAM, Philadelphia, 1988), pp. 128-137.
24. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.48.1507 48, 1507 (1982).
25. C. Grebogi, E. Ott, and J. A. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(83)90126-4 7, 181 (1983).
26. T. Tél, in Directions in Chaos, edited by, B. L. Hao, (World Scientific, Singapore, 1990), Vol. 3, pp. 149-211.
27. F. C. Moon and G. X. Li, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.55.1439 55, 1439 (1985).
28. C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.56.1011 56, 1011 (1986).
29. C. Grebogi, E. Ott, and J. A. Yorke, Physica D PDNPDT 0167-2789 10.1016/0167-2789(87)90078-9 24, 243 (1987).
30. N. Levinson, Ann. Math. ANMAAH 0003-486X 45, 723 (1944).
31. K. Green, B. Krauskopf, and K. Engelborghs, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(02)00656-5 173, 114 (2002).