Chaos suppression in flows using proportional pulses in the system variables

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

Volumn 54, Issue 1, 1996, Pages 198-209

  Matias M A ^a   Guemez J ^b  

^a UNIVERSITY OF SALAMANCA   (Spain)

^b UNIVERSITY OF CANTABRIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000609875     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.54.198     Document Type: Article

References (82)

1. E.A. Jackson, Perspectives of Nonlinear Dynamics (Cambridge University Press, Cambridge, 1991), Vols. 1 and 2.
2. E. Ott, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, 1993).
3. E.N. Lorenz, J. Atmos. Sci.20, 130 (1963).
4. E. Ott, C. Grebogi and J.A. Yorke, Phys. Rev. Lett.64, 1196 (1990).
5. D. Auerbach, P. Cvitanovic, J.P. Eckmann, G. Gunaratne and I. Procaccia, Phys. Rev. Lett.58, 2387 (1987);
6. P. Cvitanovic, Phys. Rev. Lett.61, 2729 (1988);
7. C. Grebogi, E. Ott and J.A. Yorke, Phys. Rev. A36, R3522 (1987).
8. T. Shinbrot, C. Grebogi, E. Ott and J.A. Yorke, Nature (London)363, 411 (1993).
9. W.L. Ditto and L.M. Pecora, Sci. Am.269, (2), 78 (1993).
10. G. Chen and X. Dong, Int. J. Bif. Chaos3, 1363 (1993).
11. K. Ogata, Modern Control Engineering (Prentice-Hall, Englewood Cliffs, 1990).
12. A. Hübler and E. Lüscher, Naturwissenschaften76, 67 (1989).
13. E. Ott, C. Grebogi, and J.A. Yorke, in CHAOS/XAOS: Soviet-American Perspectives on Nonlinear Science, edited by D.K. Campbell (AIP, New York, 1990), p. 153.
14. F.J. Romeiras, C. Grebogi, E. Ott and W.P. Dayawansa, Physica D58, 165 (1992).
15. T. Tél, J. Phys. A24, L1359 (1991).
16. Y.C. Lai and C. Grebogi, Phys. Rev. E49, 1094 (1994).
17. C. Grebogi, E. Ott and J.A. Yorke, Phys. Rev. Lett.48, 1507 (1982);
18. C. Grebogi, E. Ott and J.A. Yorke, Physica D7, 181 (1983).
19. U. Dressler and G. Nitsche, Phys. Rev. Lett.68, 1 (1992);
20. G. Nitsche and U. Dressler, Physica D58, 153 (1993).
21. D. Auerbach, C. Grebogi, E. Ott and J.A. Yorke, Phys. Rev. Lett.69, 3479 (1992).
22. E.R. Hunt, Phys. Rev. Lett.67, 1953 (1991).
23. B. Peng, V. Petrov and K. Showalter, J. Phys. Chem.95, 4957 (1991);
24. V. Petrov, B. Peng and K. Showalter, J. Phys. Chem.96, 7506 (1992).
25. R.W. Rollins, P. Parmananda and P. Sherard, Phys. Rev. E47, R780 (1993).
26. W.L. Ditto, S.N. Rauseo and M.L. Spano, Phys. Rev. Lett.65, 3211 (1990).
27. A. Azevedo and S.M. Rezende, Phys. Rev. Lett.66, 1342 (1991).
28. J. Singer, Y.Z. Wang and H.H. Bau, Phys. Rev. Lett.66, 1123 (1991).
29. R. Roy, T.W. Murphy, T.D. Maier, Z. Gills and E.R. Hunt, Phys. Rev. Lett.68, 1259 (1992).
30. V. Petrov, V. Gáspar, J. Masere and K. Showalter, Nature (London)361, 240 (1993).
31. A. Garfinkel, M.L. Spano, W.L. Ditto and J.N. Weiss, Science257, 1230 (1992).
32. S.J. Schiff, K. Jerger, D.H. Duong, T. Chang, M.L. Spano and W.L. Ditto, Nature (London)370, 615 (1994).
33. Proceedings of the First Experimental Chaos Conference, edited by S.T. Vohra, M.L. Spano, M.F. Shlesinger, L.M. Pecora, and W.L. Ditto (World Scientific, Singapore, 1992).
34. B. Hübinger, R. Doerner, W. Martienssen, M. Herdering, R. Pitka and U. Dressler, Phys. Rev. E50, 932 (1994).
35. K. Pyragas, Phys. Lett. A170, 421 (1992);
36. K. Pyragas, Phys. Lett. A181, 203 (1993).
37. K. Pyragas and A. Tamasevicius, Phys. Lett. A180, 99 (1993).
38. F.W. Schneider, R. Blittersdorf, A. Förster, T. Hauck, D. Lebender and J. Müller, J. Phys. Chem.97, 12244 (1993).
39. R. Lima and M. Pettini, Phys. Rev. A41, 726 (1990);
40. L. Fronzoni, M. Giocondo and M. Pettini, Phys. Rev. A43, 6483 (1991).
41. Y. Braiman and I. Goldhirsch, Phys. Rev. Lett.66, 2545 (1991).
42. R. Chacón and J. Díaz-Bejarano, Phys. Rev. Lett.71, 3103 (1993).
43. V.V. Alekseev and A.Y. Loskutov, Dokl. Akad. Nauk SSSR293, 1346 (1987) [Sov. Phys. Dokl.32, 270 (1987)].
44. A.Y. Loskutov and A.I. Shishmarev, Chaos4, 391 (1994).
45. Y.S. Kivshar, F. Rödelsperger and H. Benner, Phys. Rev. E49, 319 (1994).
46. M.A. Matías and J. Güémez, Phys. Rev. Lett.72, 1455 (1994).
47. J.A. Sepulchre and A. Babloyantz, Phys. Rev. E48, 945 (1993).
48. J. Güémez and M.A. Matías, Phys. Lett. A181, 29 (1993).
49. J. Güémez, J.M. Gutiérrez, A. Iglesias, and M.A. Matías, (a) Phys. Lett. A190, 429 (1994);
50. (b)J. Güémez, J.M. Gutiérrez, Physica D79, 164 (1994).
51. J.M. Gutiérrez, A. Iglesias, J. Güémez, and M.A. Matías, Int. J. Bif. Chaos (to be published).
52. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes, 2nd ed. (Cambridge University Press, Cambridge, 1992).
53. O.E. Rössler, Phys. Lett. A57, 397 (1976).
54. J.C. Sprott, Phys. Rev. E50, R647 (1994).
55. L. Stone, Nature (London)365, 617 (1993).
56. N. Samardzija, L.D. Greller and E. Wasserman, J. Chem. Phys.90, 2296 (1989).
57. D. Poland, Physica D65, 86 (1993).
58. J.L. Hindmarsh and R.M. Rose, Proc. R. Soc. London B221, 87 (1984).
59. J.L. Hindmarsh and R.M. Rose, Nature (London)296, 162 (1982).
60. R. Fitzhugh, Biophys. J.1, 445 (1961).
61. W. Wang, G. Pérez and H.A. Cerdeira, Phys. Rev. E47, 2893 (1993).
62. B. Peng, V. Petrov and K. Showalter, J. Phys. Chem.95, 4957 (1991);
63. V. Petrov, B. Peng and K. Showalter, J. Phys. Chem.96, 7506 (1992).
64. R. Miranda and E. Stone, Phys. Lett. A178, 105 (1993).
65. C.O. Weiss and R. Vilaseca, Chaos in Lasers (VCH, Weinheim, 1993).
66. C. Masoller, A.C. Sicardi-Schifino and L. Romanelli, Phys. Lett. A167, 185 (1992).
67. F. Argoul, A. Arneodo, P. Richetti, J.C. Roux and H.L. Swinney, Acc. Chem. Res.20, 436 (1987).
68. K.D. Willamowski and O.E. Rössler, Z. Naturforsch. Teil A35, 317 (1980).
69. B.D. Aguda and B.L. Clarke, J. Chem. Phys.89, 7428 (1988).
70. J. Güémez and M.A. Matías, Phys. Rev. E48, R2351 (1993);
71. J. Güémez and M.A. Matías, Phys. Rev. E51, 3059 (1995).
72. S. De Souza-Machado, R.W. Rollins, D.T. Jacobs and J.L. Hartman, Am. J. Phys.58, 321 (1990).
73. P. Holmes, Phil. Trans. R. Soc. A292, 419 (1979).
74. B.A. Huberman and J. Rudnick, Phys. Rev. Lett.45, 154 (1980).
75. J.P. Crutchfield, J.D. Farmer and B.A. Huberman, Phys. Rep.92, 45 (1982).
76. S.P. Dawson, C. Grebogi, T. Sauer and J.A. Yorke, Phys. Rev. Lett.73, 1927 (1994).
77. Omitted end note.
78. J.P. Crutchfield, J.D. Farmer, N. Packard, R. Shaw, G. Jones and R.J. Donnelly, Phys. Lett. A76, 1 (1980).
79. K. Kaneko, Physica D34, 1 (1989).
80. L. Menéndez de la Prida and R.V. Solé, Phys. Lett. A199, 65 (1995).
81. A.L. Goldberger, D.R. Rigney, and B.J. West, Sci. Am.262, (2), 43 (1990); B.J. West, Fractal Physiology and Chaos in Medicine(World Scientific, Singapore, 1990).
82. S.A. Kaufman, The Origins of Order (Oxford University Press, Oxford, 1993).