Numerical and experimental investigation of the effect of filtering on chaotic symbolic dynamics

Chaos

Volumn 13, Issue 1, 2003, Pages 410-419

  Zhu, Liqiang ^a   Lai, Ying Cheng ^a,b   Hoppensteadt, Frank C ^a,b   Bollt, Erik M ^c  

^a Arizona State University   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

^c CLARKSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037358820     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1520090     Document Type: Article

References (72)

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19. The phenomenon of synchronous chaos was pointed out in: H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983); V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Radiophys. Quantum Electron. 29, 747 (1986). It was independently discovered and it was pointed out for the first time in the following paper that the phenomenon can have potential application in nonlinear digital communication: L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990). Since then, synchronization in chaotic systems has become one of the most active research areas in nonlinear dynamics. See, for example, W. L. Ditto and K. Showalter, Chaos (Focus Issue on Control and Synchronization of Chaos) 7, 509-687 (1997).
20. The phenomenon of synchronous chaos was pointed out in: H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983); V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Radiophys. Quantum Electron. 29, 747 (1986). It was independently discovered and it was pointed out for the first time in the following paper that the phenomenon can have potential application in nonlinear digital communication: L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990). Since then, synchronization in chaotic systems has become one of the most active research areas in nonlinear dynamics. See, for example, W. L. Ditto and K. Showalter, Chaos (Focus Issue on Control and Synchronization of Chaos) 7, 509-687 (1997).
21. The phenomenon of synchronous chaos was pointed out in: H. Fujisaka and T. Yamada, Prog. Theor. Phys. 69, 32 (1983); V. S. Afraimovich, N. N. Verichev, and M. I. Rabinovich, Radiophys. Quantum Electron. 29, 747 (1986). It was independently discovered and it was pointed out for the first time in the following paper that the phenomenon can have potential application in nonlinear digital communication: L. M. Pecora and T. L. Carroll, Phys. Rev. Lett. 64, 821 (1990). Since then, synchronization in chaotic systems has become one of the most active research areas in nonlinear dynamics. See, for example, W. L. Ditto and K. Showalter, Chaos (Focus Issue on Control and Synchronization of Chaos) 7, 509-687 (1997).
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33. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
34. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
35. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
36. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
37. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
38. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
39. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
40. Symbolic dynamics can be a powerful tool for analyzing chaotic time series. See, for example, H. Herzel, W. Ebeling, and A. O. Schmitt, Phys. Rev. E 50, 5061 (1994); J. Kurths, A. Voss, P. Saparin, and A. Witt, Chaos 5, 88 (1995); A. Neiman, B. Shulgin, V. Anishchenko, W. Ebeling, L. Schimansky-Geier, and J. Freund, Phys. Rev. Lett. 76, 4299 (1996); R. Engbert, C. Scheffczyk, R. Krampe, J. Kurths, and R. Kliegl, in Nonlinear Time Series Analysis of Physiological Data, edited by H. Kantz, J. Kurths, and G. Mayer-Kress (Springer, Heidelberg, 1998); M. Lehrman and A. B. Rechester, Phys. Rev. Lett. 78, 1 (1997); K. Mischaikow, M. Mrozek, J. Reiss, and A. Szymczak, ibid. 82, 1144 (1999); M. B. Kennel and A. I. Mees, Phys. Rev. E 61, 2563 (2000); R. Steuer, W. Ebeling, D. F. Russell, S. Bahar, A. Neiman, and F. Moss, ibid. 64, 061911 (2001); C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
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