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Effect of Different Shape of Periodic Forces on Chaotic Oscillation in Brusselator Chemical System

Received: 20 May 2015     Accepted: 6 June 2015     Published: 23 June 2015
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Abstract

Bifurcations of periodic orbits and chaos in the Brusselator chemical reaction with different shape of external periodic forces are studied numerically. The external periodic forces considered are sine wave, square-wave, rectified sine wave, symmetric saw-tooth wave, asymmetric saw-tooth wave and modulus of sine wave. Period doubling bifurcations, chaos, reverse period doubling bifurcations, quasiperiodic bifurcations are found to occur due to the applied forces. Parametric regimes where suppression of chaos occurs are predicted. Numerical investigations including bifurcation diagram, maximal Lyapunov exponent, Poincare map, Phase portrait and time series plot are used to detect chaos, quasiperiodic and periodic orbits.

Published in International Journal of Computational and Theoretical Chemistry (Volume 3, Issue 3)
DOI 10.11648/j.ijctc.20150303.11
Page(s) 19-27
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Brusselator, Various Periodic Forces, Bifurcations, Chaos, Quasiperiodic Orbit

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Cite This Article
  • APA Style

    Guruparan S., Ravindran Durai Nayagam B., Jeyakumari S., Chinnathambi V. (2015). Effect of Different Shape of Periodic Forces on Chaotic Oscillation in Brusselator Chemical System. International Journal of Computational and Theoretical Chemistry, 3(3), 19-27. https://doi.org/10.11648/j.ijctc.20150303.11

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    ACS Style

    Guruparan S.; Ravindran Durai Nayagam B.; Jeyakumari S.; Chinnathambi V. Effect of Different Shape of Periodic Forces on Chaotic Oscillation in Brusselator Chemical System. Int. J. Comput. Theor. Chem. 2015, 3(3), 19-27. doi: 10.11648/j.ijctc.20150303.11

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    AMA Style

    Guruparan S., Ravindran Durai Nayagam B., Jeyakumari S., Chinnathambi V. Effect of Different Shape of Periodic Forces on Chaotic Oscillation in Brusselator Chemical System. Int J Comput Theor Chem. 2015;3(3):19-27. doi: 10.11648/j.ijctc.20150303.11

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  • @article{10.11648/j.ijctc.20150303.11,
      author = {Guruparan S. and Ravindran Durai Nayagam B. and Jeyakumari S. and Chinnathambi V.},
      title = {Effect of Different Shape of Periodic Forces on Chaotic Oscillation in Brusselator Chemical System},
      journal = {International Journal of Computational and Theoretical Chemistry},
      volume = {3},
      number = {3},
      pages = {19-27},
      doi = {10.11648/j.ijctc.20150303.11},
      url = {https://doi.org/10.11648/j.ijctc.20150303.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijctc.20150303.11},
      abstract = {Bifurcations of periodic orbits and chaos in the Brusselator chemical reaction with different shape of external periodic forces are studied numerically. The external periodic forces considered are sine wave, square-wave, rectified sine wave, symmetric saw-tooth wave, asymmetric saw-tooth wave and modulus of sine wave. Period doubling bifurcations, chaos, reverse period doubling bifurcations, quasiperiodic bifurcations are found to occur due to the applied forces. Parametric regimes where suppression of chaos occurs are predicted. Numerical investigations including bifurcation diagram, maximal Lyapunov exponent, Poincare map, Phase portrait and time series plot are used to detect chaos, quasiperiodic and periodic orbits.},
     year = {2015}
    }
    

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  • TY  - JOUR
    T1  - Effect of Different Shape of Periodic Forces on Chaotic Oscillation in Brusselator Chemical System
    AU  - Guruparan S.
    AU  - Ravindran Durai Nayagam B.
    AU  - Jeyakumari S.
    AU  - Chinnathambi V.
    Y1  - 2015/06/23
    PY  - 2015
    N1  - https://doi.org/10.11648/j.ijctc.20150303.11
    DO  - 10.11648/j.ijctc.20150303.11
    T2  - International Journal of Computational and Theoretical Chemistry
    JF  - International Journal of Computational and Theoretical Chemistry
    JO  - International Journal of Computational and Theoretical Chemistry
    SP  - 19
    EP  - 27
    PB  - Science Publishing Group
    SN  - 2376-7308
    UR  - https://doi.org/10.11648/j.ijctc.20150303.11
    AB  - Bifurcations of periodic orbits and chaos in the Brusselator chemical reaction with different shape of external periodic forces are studied numerically. The external periodic forces considered are sine wave, square-wave, rectified sine wave, symmetric saw-tooth wave, asymmetric saw-tooth wave and modulus of sine wave. Period doubling bifurcations, chaos, reverse period doubling bifurcations, quasiperiodic bifurcations are found to occur due to the applied forces. Parametric regimes where suppression of chaos occurs are predicted. Numerical investigations including bifurcation diagram, maximal Lyapunov exponent, Poincare map, Phase portrait and time series plot are used to detect chaos, quasiperiodic and periodic orbits.
    VL  - 3
    IS  - 3
    ER  - 

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Author Information
  • Department of Chemistry, Sri K. G. S Arts College, Srivaikuntam, Tamilnadu, India

  • Department of Chemistry, Pope’s College, Sawyerpuram, Tamilnadu, India

  • Department of Physics, Sri K. G. S Arts College, Srivaikuntam, Tamilnadu, India

  • Department of Physics, Sri K. G. S Arts College, Srivaikuntam, Tamilnadu, India

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