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Controlling Chaos

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Chaos for Engineers

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Abstract

As was shown in previous chapter chaos occurs widely in engineering and natural systems; historically it has usually been regarded as a nuisance and designed out if possible. It has been noted only as irregular or unpredictable behaviour, and often attributed to random external influences. More recently there have been examples of the potential usefulness of chaotic behaviour. It is to the potential usefulness of chaotic behaviour that we turn our attention in this chapter.

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References

  1. Ott, E, Grebogi, C., Yorke, J.A. (1990): Controlling chaos, Phys. Rev. Lett., 64, 1196–1199

    Article  MathSciNet  MATH  Google Scholar 

  2. Romeiras, F., Ott, E., Grebogi, C., Dayawansa, W.P. (1992): Controlling chaotic dynamical system, Physica, 58D, 165–180

    MathSciNet  Google Scholar 

  3. Ogorzalek, M. (1994): Chaos control: How to avoid chaos or take advantage of it, J. Franklin Inst., 331B, 681–704

    Article  MathSciNet  MATH  Google Scholar 

  4. Ditto, W.L., Rauseo, S.W., Spano, M.L. (1991): Experimental control of chaos, Phys. Rev. Lett., 65, 3211–3216

    Article  Google Scholar 

  5. Hunt, E.H. (1991): Stabilizing high-periodic orbits in a chaotic system: the diode resonator, Phys.Rev. Lett., 67, 1953–1959

    Article  Google Scholar 

  6. Mehta, N., Henderson, R. (191): Controlling chaos to generate aperiodic orbit, Phys. Rev., 44A, 4861–4869

    MathSciNet  Google Scholar 

  7. Tel, T. (1991): Controlling transient chaos, J. Phys. A., 24, 11359–11365

    Article  MathSciNet  Google Scholar 

  8. Dressier, V., Nitsche, G. (1992): Controlling chaos using time delay coordinates, Phys. Rev. Lett., 68, 1–5

    Article  Google Scholar 

  9. Singer, J., Wang, Y.-Z., Bau, H.H. (1991): Controlling a chaotic system, Phys. Rev. Lett., 66, 1123–1126

    Article  Google Scholar 

  10. Pyragas, K. (1992): Continuous control of chaos by self-controlling feedback, Phys. Lett., 170A, 421–427

    Google Scholar 

  11. Ueda, Y. (1979): Randomly transitional phenomena in the system governed by Duffing’s equation, J. Stat. Phys., 20, 181–196

    Article  MathSciNet  Google Scholar 

  12. Kapitaniak, T. (1991): Chaotic Oscillations in Mechanical Systems, Manchester University Press, Manchester

    MATH  Google Scholar 

  13. Wolf, A., Swift, J., Swinney, H. and Vastano, A. (1985): Determining Lyapunov exponents from time series, Physica, 16D 285–314

    MathSciNet  Google Scholar 

  14. Kapitaniak, T. (1996): Controlling Chaos, Academic Press, London

    MATH  Google Scholar 

  15. Chen, G., Dong, X. (1998): From Chaos to Order, World Scientific, Singapore

    MATH  Google Scholar 

  16. Schuster, H.G. (1999): Handbook of Chaos Control, J. Wiley and Sons, Chichester

    Book  MATH  Google Scholar 

  17. Pecora, L., Carroll, T. (1990): Synchronization in chaotic systems, Phys. Rev. Lett., 64, 821–825

    Article  MathSciNet  Google Scholar 

  18. Chua, L.O., Kocarev, L., Eckert, K. and Itoh, M. (1992): Experimental chaos synchronization in Chua’s circuit, Int. J. Bif. Chaos, 2, 705–712

    Article  MATH  Google Scholar 

  19. Kapitaniak, T. Chua, L.O., Zhong, G.Q. (1994): Experimental synchronization of chaos using continuous control, Int. J. Bif. Chaos, 4, 483–488

    Article  MATH  Google Scholar 

  20. Qu, Z., Hu, G., Ma, B. (1993): Note on continuous chaos control, Phys., Lett., 178A, 265–272

    MathSciNet  Google Scholar 

  21. Cuomo, K., Oppenheim, A. (1993): Circuit implementation of synchronized chaos with applications to communication, Phys. Rev. Lett., 71, 65–69

    Article  Google Scholar 

  22. Kocarev, L. Halle, K., Eckert, K., Chua, L.O. (1992): Experimental demonstration of secure communications via chaos synchronization, Int. J. Bif. Chaos, 2, 709–716

    Article  MATH  Google Scholar 

  23. Halle, K., Wu, C.W., Itoh, M. and Chua L.O. (1993): Spread spectrum communication though modulation of chaos, Int. J. Bifurcat. Chaos, 3, 469–477

    Article  MATH  Google Scholar 

  24. Parlitz, V., Lauterborn, W. (1987): Period-doubling cascades and devil’s staircase of the driven van der Pol oscillator, Phys. Rev., 36A, 1428–1434

    Google Scholar 

  25. Perez, G. and Cerdeira, H. (1995): Extracting messages masked by chaos, Phys. Rev. Lett. 74, 1970–1973

    Article  Google Scholar 

  26. Popp, K. and Stelter, P. (1990): Nonlinear oscillations of structures induced by dry friction, in: Non-linear Dynamics in Engineering Systems, ed. W. Schiehlen, Springer, New York

    Google Scholar 

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Authors and Affiliations

  1. Division of Dynamics, Technical University of Lodz, Stefanowskiego 1/15, 90-924, Lodz, Poland

    Professor Tomasz Kapitaniak

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  1. Professor Tomasz Kapitaniak
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© 2000 Springer-Verlag Berlin Heidelberg

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Kapitaniak, T. (2000). Controlling Chaos. In: Chaos for Engineers. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-57143-5_7

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  • DOI: https://doi.org/10.1007/978-3-642-57143-5_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66574-8

  • Online ISBN: 978-3-642-57143-5

  • eBook Packages: Springer Book Archive

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