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Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method

Received: 13 October 2016     Accepted: 3 November 2016     Published: 12 January 2017
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Abstract

This paper presents three important phenomena of chaos synchronization between two different hyperchaotic systems using nonlinear adaptive control strategy. In detailed, complete synchronization, anti- synchronization and hybrid synchronization with nine unknown parameters. Modified hyperchaotic Pan system is consider as drive and hyperchaotic Liu system as response system. Stabilization of error dynamics for each phenomenon is realized by satisfying Lyapunov's second method as a main tool. Theoretical analysis and numerical simulations are shown to verify the results.

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1)
DOI 10.11648/j.ijtam.20170301.16
Page(s) 36-42
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), 2017. Published by Science Publishing Group

Keywords

Complete Synchronization, Anti-synchronization, Hybrid Synchronization, Nonlinear Dynamical Systems, Adaptive Control, Lyapunov's Second Method

References
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[2] M. M. Aziz., S. F. AL-Azzawi, Chaos control and synchronization of a novel 5-D hyperchaotic Lorenz system via nonlinear control, Int. J. Mode. Phys. Appli., 2, (2015) 110-115.
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[6] F. Q. Dou, J. A. Sun, W. S. Duan, K. P. Lu ̈, Controlling hyperchaos in the new hyperchaotic system, Commun. Nonlinear Sci. Numer., 14 (2009) 552-559.
[7] E. M. Elabbasy, H. N. Agiza, M. M. El-Dessoky, Global Chaos synchronization for four – scroll attractor by nonlinear control. Scientific Research and Essay, 1 (2006) 65-71.
[8] Q. Jia, Hyperchaos synchronization between two different hyperchaotic systems, Journal of Information and Computing. Science, 3 (2008) 73–80.
[9] A. Khan, P. Singh, Chaos synchronization in Lorenz system, Appl. Math., 6 (2015), 1864-1872.
[10] D. Lu, A. Wang, X. Tian, Control and synchronization of a new hyperchaotic system with unknown parameters, International Journal of Nonlinear Science. 6 (2008) 224-229.
[11] L. Pan, W. Zhou, L. Zhou, K. Sun, Chaos synchronization between two different fractional-order hyperchaotic systems, J, Commun. Nonlinear Sci. Numer. Simulat., 16 (2011), 2628–2640.
[12] J. H. Park, Chaos synchronization of a chaotic system via nonlinear control, Chaos Solitons Fractals 25 (2005) 579-584.
[13] F. Q. Dou, J. A. Sun, W. S. Duan, Anti-synchronization in different hyperchaotic systems, Commun. Theor. Phys., 50 (2008) 907-912.
[14] P. P. Singh, J. P. Singh, B. K. Roy, Synchronization and anti- synchronization of Lu ̈ and Bhalekar-Gejji chaotic systems using nonlinear active control. Chaos, Solitons and Fractals, 69 (2014) 31-39.
[15] M. Srivastava, S. P. Ansari, S. K. Agrawal, S. Das, A. Y. T. Leung, Anti- synchronization between identical and non-identical fractional-order chaotic systems using active control method, Nonlinear Dyn. 76 (2014) 905-914.
[16] K. S. Sudheer, M. Sabir, Hybrid synchronization of hyperchaotic Lü system, Pramana J. Phys.73 (2009) 781-786.
[17] G. Xu, S. Chen, Hybrid synchronization of a Chen hyperchaotic system with two simple linear feedback controllers Appl. Math., 4 (2013), 13-17.
[18] M. M. Aziz., S. F. AL-Azzawi, Control and synchronization with known and unknown parameters, Appl. Math., 7 (2016), 292-303.
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Cite This Article
  • APA Style

    Maysoon M. Aziz, Saad Fawzi Al-Azzawi. (2017). Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method. International Journal of Theoretical and Applied Mathematics, 3(1), 36-42. https://doi.org/10.11648/j.ijtam.20170301.16

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    ACS Style

    Maysoon M. Aziz; Saad Fawzi Al-Azzawi. Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method. Int. J. Theor. Appl. Math. 2017, 3(1), 36-42. doi: 10.11648/j.ijtam.20170301.16

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    AMA Style

    Maysoon M. Aziz, Saad Fawzi Al-Azzawi. Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method. Int J Theor Appl Math. 2017;3(1):36-42. doi: 10.11648/j.ijtam.20170301.16

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  • @article{10.11648/j.ijtam.20170301.16,
      author = {Maysoon M. Aziz and Saad Fawzi Al-Azzawi},
      title = {Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {3},
      number = {1},
      pages = {36-42},
      doi = {10.11648/j.ijtam.20170301.16},
      url = {https://doi.org/10.11648/j.ijtam.20170301.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170301.16},
      abstract = {This paper presents three important phenomena of chaos synchronization between two different hyperchaotic systems using nonlinear adaptive control strategy. In detailed, complete synchronization, anti- synchronization and hybrid synchronization with nine unknown parameters. Modified hyperchaotic Pan system is consider as drive and hyperchaotic Liu system as response system. Stabilization of error dynamics for each phenomenon is realized by satisfying Lyapunov's second method as a main tool. Theoretical analysis and numerical simulations are shown to verify the results.},
     year = {2017}
    }
    

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    T1  - Three Important Phenomena of Chaos Synchronization Between Two Different Hyperchaotic Systems via Adaptive Control Method
    AU  - Maysoon M. Aziz
    AU  - Saad Fawzi Al-Azzawi
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    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
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    EP  - 42
    PB  - Science Publishing Group
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    UR  - https://doi.org/10.11648/j.ijtam.20170301.16
    AB  - This paper presents three important phenomena of chaos synchronization between two different hyperchaotic systems using nonlinear adaptive control strategy. In detailed, complete synchronization, anti- synchronization and hybrid synchronization with nine unknown parameters. Modified hyperchaotic Pan system is consider as drive and hyperchaotic Liu system as response system. Stabilization of error dynamics for each phenomenon is realized by satisfying Lyapunov's second method as a main tool. Theoretical analysis and numerical simulations are shown to verify the results.
    VL  - 3
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq

  • Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq

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