Control and synchronization of chaos in high dimensional systems: Review of some recent results

Chaos

Volumn 7, Issue 4, 1997, Pages 644-652

  Ding, Mingzhou ^a   Ding, E Jiang ^b,c   Ditto, William L ^d   Gluckman, Bruce ^e   In, Visarath ^f   Peng, Jian Hua ^g   Spano, Mark L ^f   Yang, Weiming ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

^b BEIJING NORMAL UNIVERSITY   (China)

^c CCAST WORLD LABORATORY   (China)

^d GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^e CHILDREN'S NATIONAL MEDICAL CENTER   (United States)

^f NAVAL SURFACE WARFARE CENTER   (United States)

^g NORTHEAST NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040453558     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.166284     Document Type: Article

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37. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
38. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
39. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
40. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
41. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
42. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
43. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
44. For a sample of works dealing with chaos control in high dimensions, see F. J. Romeiras, C. Grebogi, E. Ott, and W. P. Dayawansa, Physica D 58, 165 (1992); D. Auerbach, C. Grebogi, E. Ott, and J. A. Yorke, Phys. Rev. Lett. 69, 3479 (1992); J. A. Sepulchre and A. Babloyantz, Phys. Rev. E 48, 945 (1993); G. Hu and K. He, Phys. Rev. Lett. 71, 3794 (1993); C. Reyl, L. Flepp, R. Badii, and E. Brun, Phys. Rev. E 47, 267 (1993); P. Colet, R. Roy, and K. Wiesenfeld, Phys. Rev. E 50, 3453 (1994); G. Hu and Z. Qu, Phys. Rev. Lett. 72, 68 (1994); I. B. Schwartz and I. Tiandaf, Phys. Rev. E 50, 2548 (1994); A. Namajunas, K. Pyragas, and A. Tamasevicius, Phys. Lett. A 204, 255 (1995); M. E. Bleich and J. E. S. Socolar, Phys. Rev. E 54, R17 (1996); D. J. Christini, J. J. Collins, and P. Linsay, Phys. Rev. 54, 4824 (1996).
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55. T. L. Carroll, I. Triandaf, I. B. Schwartz, and L. M. Pecora, Phys. Rev. A 46, 6189 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); I. Triandaf and I. B. Schwartz, Phys. Rev. E 48, 718 (1993); S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993); N. F. Rulkov, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 50, 314 (1994); V. Petrov, M. J. Crowley, and K. Showalter, Phys. Rev. Lett. 72, 2955 (1994); V. In. W. L. Ditto, and M. L. Spano, Phys. Rev. E 51, R2689 (1995); U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen, Phys. Rev. E 51, 1845 (1995); K. Konishi and H. Kokame, Phys. Rev. A 206, 203 (1995).
56. T. L. Carroll, I. Triandaf, I. B. Schwartz, and L. M. Pecora, Phys. Rev. A 46, 6189 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); I. Triandaf and I. B. Schwartz, Phys. Rev. E 48, 718 (1993); S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993); N. F. Rulkov, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 50, 314 (1994); V. Petrov, M. J. Crowley, and K. Showalter, Phys. Rev. Lett. 72, 2955 (1994); V. In. W. L. Ditto, and M. L. Spano, Phys. Rev. E 51, R2689 (1995); U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen, Phys. Rev. E 51, 1845 (1995); K. Konishi and H. Kokame, Phys. Rev. A 206, 203 (1995).
57. T. L. Carroll, I. Triandaf, I. B. Schwartz, and L. M. Pecora, Phys. Rev. A 46, 6189 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); I. Triandaf and I. B. Schwartz, Phys. Rev. E 48, 718 (1993); S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993); N. F. Rulkov, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 50, 314 (1994); V. Petrov, M. J. Crowley, and K. Showalter, Phys. Rev. Lett. 72, 2955 (1994); V. In. W. L. Ditto, and M. L. Spano, Phys. Rev. E 51, R2689 (1995); U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen, Phys. Rev. E 51, 1845 (1995); K. Konishi and H. Kokame, Phys. Rev. A 206, 203 (1995).
58. T. L. Carroll, I. Triandaf, I. B. Schwartz, and L. M. Pecora, Phys. Rev. A 46, 6189 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); I. Triandaf and I. B. Schwartz, Phys. Rev. E 48, 718 (1993); S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993); N. F. Rulkov, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 50, 314 (1994); V. Petrov, M. J. Crowley, and K. Showalter, Phys. Rev. Lett. 72, 2955 (1994); V. In. W. L. Ditto, and M. L. Spano, Phys. Rev. E 51, R2689 (1995); U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen, Phys. Rev. E 51, 1845 (1995); K. Konishi and H. Kokame, Phys. Rev. A 206, 203 (1995).
59. T. L. Carroll, I. Triandaf, I. B. Schwartz, and L. M. Pecora, Phys. Rev. A 46, 6189 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); I. Triandaf and I. B. Schwartz, Phys. Rev. E 48, 718 (1993); S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993); N. F. Rulkov, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 50, 314 (1994); V. Petrov, M. J. Crowley, and K. Showalter, Phys. Rev. Lett. 72, 2955 (1994); V. In. W. L. Ditto, and M. L. Spano, Phys. Rev. E 51, R2689 (1995); U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen, Phys. Rev. E 51, 1845 (1995); K. Konishi and H. Kokame, Phys. Rev. A 206, 203 (1995).
60. T. L. Carroll, I. Triandaf, I. B. Schwartz, and L. M. Pecora, Phys. Rev. A 46, 6189 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); I. Triandaf and I. B. Schwartz, Phys. Rev. E 48, 718 (1993); S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993); N. F. Rulkov, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 50, 314 (1994); V. Petrov, M. J. Crowley, and K. Showalter, Phys. Rev. Lett. 72, 2955 (1994); V. In. W. L. Ditto, and M. L. Spano, Phys. Rev. E 51, R2689 (1995); U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen, Phys. Rev. E 51, 1845 (1995); K. Konishi and H. Kokame, Phys. Rev. A 206, 203 (1995).
61. T. L. Carroll, I. Triandaf, I. B. Schwartz, and L. M. Pecora, Phys. Rev. A 46, 6189 (1992); Z. Gills, C. Iwata, R. Roy, I. B. Schwartz, and I. Triandaf, Phys. Rev. Lett. 69, 3169 (1992); I. Triandaf and I. B. Schwartz, Phys. Rev. E 48, 718 (1993); S. Bielawski, M. Bouazaoui, D. Derozier, and P. Glorieux, Phys. Rev. A 47, 3276 (1993); N. F. Rulkov, L. S. Tsimring, and H. D. I. Abarbanel, Phys. Rev. E 50, 314 (1994); V. Petrov, M. J. Crowley, and K. Showalter, Phys. Rev. Lett. 72, 2955 (1994); V. In. W. L. Ditto, and M. L. Spano, Phys. Rev. E 51, R2689 (1995); U. Dressler, T. Ritz, A. Schenck zu Schweinsberg, R. Doerner, B. Hübinger, and W. Martienssen, Phys. Rev. E 51, 1845 (1995); K. Konishi and H. Kokame, Phys. Rev. A 206, 203 (1995).
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65. R. He and P. G. Vaidya, Phys. Rev. A 46, 7387 (1992); M. de Sousa Vieira, A. J. Lichtenherg, and M. A. Lieberman, Phys. Rev. A 46, R7359 (1992); K. Pyragas, Phys. Lett. A 181, 203 (1992); U. Parlitz et al., Int. J. Bifurcations Chaos 4, 973 (1992); Lj. Kocarev et al., ibid. 2, 709 (1992); Y. C. Lai and C. Grebogi, Phys. Rev. E 47, 2357 (1993); T. C. Newell et al., Phys. Rev. Lett. 72, 1647 (1994); ibid. Phys. Rev. E 49, 313 (1994); M. Ding and E. Ott, Phys. Rev. E 49, R945 (1994); R. Brown, N. F. Rulkov, and N. B. Tufillaro, Phys. Rev. E 50, 4488 (1994); Lj. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. Gershenfeld and G. Grinstein, ibid. 74, 5024 (1995).
66. R. He and P. G. Vaidya, Phys. Rev. A 46, 7387 (1992); M. de Sousa Vieira, A. J. Lichtenherg, and M. A. Lieberman, Phys. Rev. A 46, R7359 (1992); K. Pyragas, Phys. Lett. A 181, 203 (1992); U. Parlitz et al., Int. J. Bifurcations Chaos 4, 973 (1992); Lj. Kocarev et al., ibid. 2, 709 (1992); Y. C. Lai and C. Grebogi, Phys. Rev. E 47, 2357 (1993); T. C. Newell et al., Phys. Rev. Lett. 72, 1647 (1994); ibid. Phys. Rev. E 49, 313 (1994); M. Ding and E. Ott, Phys. Rev. E 49, R945 (1994); R. Brown, N. F. Rulkov, and N. B. Tufillaro, Phys. Rev. E 50, 4488 (1994); Lj. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. Gershenfeld and G. Grinstein, ibid. 74, 5024 (1995).
67. R. He and P. G. Vaidya, Phys. Rev. A 46, 7387 (1992); M. de Sousa Vieira, A. J. Lichtenherg, and M. A. Lieberman, Phys. Rev. A 46, R7359 (1992); K. Pyragas, Phys. Lett. A 181, 203 (1992); U. Parlitz et al., Int. J. Bifurcations Chaos 4, 973 (1992); Lj. Kocarev et al., ibid. 2, 709 (1992); Y. C. Lai and C. Grebogi, Phys. Rev. E 47, 2357 (1993); T. C. Newell et al., Phys. Rev. Lett. 72, 1647 (1994); ibid. Phys. Rev. E 49, 313 (1994); M. Ding and E. Ott, Phys. Rev. E 49, R945 (1994); R. Brown, N. F. Rulkov, and N. B. Tufillaro, Phys. Rev. E 50, 4488 (1994); Lj. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. Gershenfeld and G. Grinstein, ibid. 74, 5024 (1995).
68. R. He and P. G. Vaidya, Phys. Rev. A 46, 7387 (1992); M. de Sousa Vieira, A. J. Lichtenherg, and M. A. Lieberman, Phys. Rev. A 46, R7359 (1992); K. Pyragas, Phys. Lett. A 181, 203 (1992); U. Parlitz et al., Int. J. Bifurcations Chaos 4, 973 (1992); Lj. Kocarev et al., ibid. 2, 709 (1992); Y. C. Lai and C. Grebogi, Phys. Rev. E 47, 2357 (1993); T. C. Newell et al., Phys. Rev. Lett. 72, 1647 (1994); ibid. Phys. Rev. E 49, 313 (1994); M. Ding and E. Ott, Phys. Rev. E 49, R945 (1994); R. Brown, N. F. Rulkov, and N. B. Tufillaro, Phys. Rev. E 50, 4488 (1994); Lj. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. Gershenfeld and G. Grinstein, ibid. 74, 5024 (1995).
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70. R. He and P. G. Vaidya, Phys. Rev. A 46, 7387 (1992); M. de Sousa Vieira, A. J. Lichtenherg, and M. A. Lieberman, Phys. Rev. A 46, R7359 (1992); K. Pyragas, Phys. Lett. A 181, 203 (1992); U. Parlitz et al., Int. J. Bifurcations Chaos 4, 973 (1992); Lj. Kocarev et al., ibid. 2, 709 (1992); Y. C. Lai and C. Grebogi, Phys. Rev. E 47, 2357 (1993); T. C. Newell et al., Phys. Rev. Lett. 72, 1647 (1994); ibid. Phys. Rev. E 49, 313 (1994); M. Ding and E. Ott, Phys. Rev. E 49, R945 (1994); R. Brown, N. F. Rulkov, and N. B. Tufillaro, Phys. Rev. E 50, 4488 (1994); Lj. Kocarev and U. Parlitz, Phys. Rev. Lett. 74, 5028 (1995); N. Gershenfeld and G. Grinstein, ibid. 74, 5024 (1995).
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