Controlling chaos in low- and high-dimensional systems with periodic parametric perturbations

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

Volumn 59, Issue 5, 1999, Pages 5313-5324

  Mirus, K A ^a   Sprott, J C ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000232533     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.5313     Document Type: Article

References (81)

1. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
2. W. L. Ditto, S. N. Rauseo, and M. L. Spano, Phys. Rev. Lett. 65, 3211 (1990).
3. P. M. Alsing, A. Gavrielides, and V. Kovanis, Phys. Rev. E 50, 1968 (1994).
4. U. Dressler and G. Nitsche, Phys. Rev. Lett. 68, 1 (1992).
5. B. Cazelles, G. Boudjema, and N. P. Chau, Phys. Lett. A 196, 326 (1995).
6. B. Hubinger, R. Doerner, W. Martienssen, M. Herdering, R. Pitka, and U. Dressler, Phys. Rev. E 50, 932 (1994).
7. D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992).
8. T. Shinbrot, W. Ditto, C. Grebogi, E. Ott, M. Spano, and J. A. Yorke, Phys. Rev. Lett. 68, 2863 (1992).
9. E. R. Hunt, Phys. Rev. Lett. 67, 1953 (1991).
10. R. Roy, T. W. Murphy, Jr., T. D. Maier, Z. Gills, and E. R. Hunt, Phys. Rev. Lett. 68, 1259 (1992).
11. K. Pyragas, Phys. Lett. A 170, 421 (1992).
12. U. Dressler and G. Nitsche, Phys. Rev. Lett. 68, 1 (1992).
13. Y. Liu, L. C. Barbosa, and J. R. Leite, Phys. Lett. A 193, 259 (1994).
14. M. A. Matias and J. Guemez, Phys. Rev. Lett. 72, 1455 (1994).
15. Y. H. Chen and M. Y. Chou, Phys. Rev. E 50, 2331 (1994).
16. C.-C. Fuh and P.-C. Tung, Phys. Rev. Lett. 75, 2952 (1995).
17. J. Schweizer and M. P. Kennedy, Phys. Rev. E 52, 4865 (1995).
18. J. Alvarez-Ramirez, Phys. Rev. E 50, 2339 (1994).
19. J. L. Breeden, Phys. Lett. A 190, 264 (1994).
20. J. L. Breeden, F. Dinkelacker, and A. Hübler, Phys. Rev. A 42, 5827 (1990).
21. S. Fahy and D. R. Hamann, Phys. Rev. Lett. 69, 761 (1992).
22. Y.-Y. Chen, Phys. Rev. Lett. 77, 4318 (1996).
23. L. Molgedey, J. Schuchhardt, and H. G. Schuster, Phys. Rev. Lett. 69, 3717 (1992).
24. V. Hakim and W.-J. Rappel, Europhys. Lett. 27, 637 (1994).
25. A. Maritan and J. R. Banavar, Phys. Rev. Lett. 72, 1451 (1994).
26. L. M. Pecora and T. L. Caroll, Phys. Rev. Lett. 64, 821 (1990).
27. L. M. Pecora and T. L. Caroll, Phys. Rev. A 44, 2374 (1991).
28. Y. Liu and L. C. Barbosa, Phys. Lett. A 197, 13 (1995).
29. S. Varma and V. S. Varma, Phys. Rev. E 48, 1670 (1993).
30. A. Y. Loskutov and A. I. Shishmarev, Chaos 4, 391 (1994).
31. R.-R. Hsu, H.-T. Su, J.-L. Chern, and C.-C. Chen, Phys. Rev. Lett. 78, 2936 (1997).
32. J. Rössler, M. Kiwi, B. Hess, and M. Markus, Phys. Rev. A 39, 5954 (1989).
33. M. Lücke and Y. Saito, Phys. Lett. 91A, 205 (1982).
34. E. A. Jackson and A. Hübler, Physica D 44, 407 (1990).
35. V. V. Alekseev and A. Y. Loskutov, Dokl. Akad. Nauk (SSSR) 293 1346 (1987) [Sov. Phys. Dokl. 32, 270 (1987)].
36. R. Lima and M. Pettini, Phys. Rev. A 41, 726 (1990).
37. Z. Qu, G. Hu, G. Yang, and G. Qin, Phys. Rev. Lett. 74, 1736 (1995).
38. Y. S. Kivshar, F. Rödelsperger, and H. Benner, Phys. Rev. E 49, 319 (1994).
39. L. Fronzoni, M. Giocondo, and M. Pettini, Phys. Rev. A 43, 6483 (1991).
40. Y. Braimin and I. Goldhirsch, Phys. Rev. Lett. 66, 2545 (1991).
41. R. Chacón, Phys. Rev. E 50, 750 (1994).
42. R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi, Phys. Rev. E 49, 2528 (1994).
43. J. Simonet, M. Warden, and E. Brun, Phys. Rev. E 50, 3383 (1994).
44. Y. Liu, N. Kikuchi, and J. Ohtsubo, Phys. Rev. E 51, 2697 (1995).
45. S. T. Vorha, L. Fabiny, and F. Bucholtz, Phys. Rev. Lett. 75, 65 (1995).
46. A. Azevedo and S. M. Rezende, Phys. Rev. Lett. 66, 1342 (1991).
47. H.-E. Sätherblom, Phys. Plasmas 4, 174 (1997).
48. W. X. Ding, H. Q. She, W. Huang, and C. X. Yu, Phys. Rev. Lett. 72, 96 (1994).
49. R. N. Dexter, D. W. Kerst, T. W. Lovell, S. C. Prager, and J. C. Sprott, Fusion Technol. 19, 131 (1991).
50. J. Kaplan and J. Yorke, in Functional Differential Equations and the Approximation of Fixed Points, edited by H. O. Peitgen and H. O. Walther, Lecture Notes in Mathematics Vol. 730 (Springer, Berlin, 1979), p. 204.
51. P. Frederickson, J. Kaplan, and J. Yorke, J. Diff. Eqns. 49, 185 (1983).
52. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano Physica D16, 285 (1985).
53. T. Y. Li and J. A. Yorke, Am. Math. Monthly 82, 985 (1975).
54. R. C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, New York, 1994).
55. M. Markus, Comput. Phys. 4, 481 (1990).
56. E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963).
57. D. P. Lathrop and E. J. Kostelich, Phys. Rev. A 40, 4028 (1989).
58. E. N. Lorenz, in Nonlinear Dynamics, Ann. (N.Y.) Acad. Sci. 357, 282 (1980), edited by R. H. G. Hellerman.
59. J. Singer, Y.-Z. Wang, and H. H. Bau, Phys. Rev. Lett. 66, 1123 (1991).
60. O. E. Rössler, Phys. Lett. 57A, 397 (1976).
61. J. C. Sprott, Phys. Rev. E 50, R647 (1994).
62. J. C. Sprott, Phys. Lett. A 228, 271 (1994).
63. J. C. Sprott, Am. J. Phys. 65, 537 (1997).
64. N. M. Lawandy, D. V. Plant, and K. Lee, Phys. Rev. A 34, 1247 (1986).
65. W. V. R. Malkus, Mèm. Soc. R. Sci. Liège Collect. in-4 IV, 125 (1972).
66. J. A. Yorke and E. D. Yorke, J. Stat. Phys. 21, 263 (1979).
67. S. H. Davis and M. N. Roppo, Physica D 24, 226 (1987).
68. E. A. Jackson and A. Kodogeorgiou, Phys. Lett. A 168, 270 (1992).
69. E. N. Lorenz, Nature (London) 353, 241 (1991).
70. T. Shinbrot, Adv. Phys. 44, 73 (1995).
71. W. Yang, M. Ding, A. J. Mandell, and E. Ott, Phys. Rev. E 51, 102 (1994).
72. D. Auerbach, Phys. Rev. Lett. 72, 1184 (1994).
73. H. G. Schuster and M. B. Stemmler, Phys. Rev. E 56, 6410 (1997).
74. R. O. Grigoriev, M. C. Cross, and H. G. Schuster, Phys. Rev. Lett. 79, 2795 (1997).
75. R. O. Grigoriev and M. C. Cross, Phys. Rev. E 57, 1550 (1998).
76. Z. Yoshida, Y. Sakuragi, and Y. Yamakoshi, J. Plasma Phys. 49, 403 (1993).
77. J. B. Taylor, Rev. Mod. Phys. 58, 741 (1986).
78. S. Assadi, S. C. Prager, and K. L. Sidikman, Phys. Rev. Lett. 69, 281 (1992).
79. A. B. Rechester and M. N. Rosenbluth, Phys. Rev. Lett. 40, 38 (1978).
80. C. A. Watts, D. E. Newman, and J. C. Sprott, Phys. Rev. E 49, 2291 (1994).
81. J. Stavans, F. Heslot, and A. Libchaber, Phys. Rev. Lett. 55, 596 (1985).