Stabilizing unstable periodic points of one-dimensional nonlinear systems using delayed-feedback signals

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 54, Issue 4, 1996, Pages 3455-3460

  Konishi, Keiji ^a   Ishii, Morio ^a   Kokame, Hideki ^a  

^a Osaka City University   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000086354     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.54.3455     Document Type: Article

References (53)

1. E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett.64, 1196 (1990).
2. E. Ott, C. Grebogi, and J. A. Yorke, CHAOS/XAOC (AIP, New York);
3. F. J. Romeiras, C. Grebogi, E. Ott and W. P. Dayawansa, Physica D58, 165 (1992).
4. B. Peng, V. Petrov and K. Showalter, J. Phys. Chem.95, 4957 (1991);
5. V. Petrov, B. Peng and K. Showalter, J. Chem. Phys.96, 7506 (1992).
6. D. Auerbach, C. Grebogi, E. Ott and J. A. Yorke, Phys. Rev. Lett.69, 3479 (1992);
7. J. A. Sepulchre and A. Babloyantz, Phys. Rev. E48, 945 (1993);
8. D. Auerbach, Phys. Rev. Lett.72, 1184 (1994);
9. V. Petrov, Phys. Rev. E51, 3988 (1995);
10. V. V. Astakhov, V. S. Anishchenko, and A. V. Shabunin, IEEE Trans Circuits Syst.CAS-42, 352 (1995).
11. G. Chen and X. Dong, IEEE Trans. Circuits Syst.CAS-40, 591 (1993).
12. K. Pyragas, Phys. Lett. A170, 421 (1992).
13. Y. C. Lai, M. Ding and C. Grebogi, Phys. Rev. E47, 86 (1993);
14. Y. C. Lai, T. Tél and C. Grebogi, Phys. Rev. E48, 709 (1993).
15. J. Singer, Y-Z. Wang and H. H. Bau, Phys. Rev. Lett.66, 1123 (1991).
16. W. L. Ditto, S. N. Rauseo and M. L. Spano, Phys. Rev. Lett.65, 3211 (1990).
17. E. R. Hunt, Phys. Rev. Lett.67, 1953 (1991);
18. G. A. Johnson, T. E. Tigner and E. R. Hunt, J. Circuits Syst. Comput.3, 109 (1993).
19. R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills and E. R. Hunt, Phys. Rev. Lett.68, 1259 (1992);
20. C. Reyl, L. Flepp, R. Badii and E. Brun, Phys. Rev. E47, 267 (1993).
21. U. Dressler and G. Nitsche, Phys. Rev. Lett.68, 1 (1992);
22. G. Nitsche and U. Dressler, Physica D58, 153 (1992).
23. P. M. Alsing, A. Gavrielides and V. Kovanis, Phys. Rev. E49, 1225 (1994);
24. K. Konishi, H. Kawabata, and Y. Takeda (unpublished).
25. K. Konishi and H. Kokame, Phys. Lett. A206, 203 (1995).
26. G. Chen, Int. J. of Bifurcation Chaos4, 461 (1994).
27. S. Bhajekar, E. Jonckheere, and A. Hammad, in Proceedings of the 33rd IEEE CDC (IEEE, New York, 1994), p. 3285.
28. B. Mensour and A. Longtin, Phys. Lett. A205, 18 (1995);
29. K. Pyragas, Phys. Lett. A206, 323 (1995);
30. A. Babloyantz, C. Lourenco and J. A. Sepulchre, Physica D86, 274 (1995);
31. M. E. Bleich and J. E. S. Socolar, Phys. Lett. A 210, 87 (1996);
32. W. Yao, Phys. Lett. A207, 349 (1995);
33. A. Kittel, J. Parisi and K. Pyragas, Phys. Lett. A198, 433 (1995);
34. T. Ushio (private communication).
35. K. Pyragas and A. Tamasevicius, Phys. Lett. A180, 99 (1993);
36. J. E. S. Socolar, D. W. Sukow and D. J. Gauthier, Phys. Rev. E50, 3245 (1994);
37. A. Namajūnas, K. Pyragas and A. Tamasevicius, Phys. Lett. A204, 255 (1995).
38. S. Bielawski, D. Derozier and P. Glorieux, Phys. Rev. E49, 971 (1994).
39. T. Hikihara and T. Kawagoshi, Phys. Lett. A211, 29 (1996).
40. T. L. Carroll, Phys. Rev. A46, 6189 (1992);
41. G. Gills, C. Iwata and R. Roy, Phys. Rev. Lett.69, 3169 (1992);
42. I. B. Schwartz and I. Triandaf, Phys. Rev. A46, 7439 (1992);
43. I. Triandaf and I. B. Schwartz, Phys. Rev. E48, 718 (1993);
44. V. Petrov, M. J. Crowley and K. Showalter, Phys. Rev. Lett.72, 2955 (1994);
45. V. Petrov, M. J. Crowley and K. Showalter, Int. J. Bifurcation Chaos4, 1311 (1994);
46. U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger and W. Martienssen, Phys. Rev. E51, 1845 (1995);
47. Visarath In, W. L. Ditto and M. L. Spano, Phys. Rev. E51, 2689 (1995).
48. S. Bielawski, D. Derozier and P. Glorieux, Phys. Rev. A47, 2492 (1993);
49. R. W. Rollins, P. Parmananda and P. Sherard, Phys. Rev. E47, 780 (1993);
50. P. V. Bayly and L. N. Virgin, Phys. Rev. E50, 604 (1994).
51. Y. Cho and T. Umeda, Opt. Commun.59, 131 (1986);
52. J. Simonet, E. Brun and R. Badii, Phys. Rev. E52, 2294 (1995).
53. M. C. Mackey and L. Glass, Science197, 287 (1977).