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Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems

Received: 22 September 2016     Accepted: 1 November 2016     Published: 30 November 2016
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Abstract

Three important phenomena of chaos synchronization are considered in this paper, In detailed, complete synchronization, anti- synchronization and hybrid synchronization based on the nonlinear active control approach between two different (non-identical) 4D hyperchaotic systems, i. e. Modified Pan and Liu are study herein. The Modified hyperchaotic Pan system is taken as drive system and hyperchaotic Liu system as response. Stabilization of error dynamics for each phenomenon is realized by satisfying two analytical approaches; Lyapunov's second method and linear system theory. Controllers are designed by using the relevant variable of drive and response systems. Theoretical analysis and numerical simulations are shown to verify the results.

Published in Mathematics Letters (Volume 2, Issue 5)
DOI 10.11648/j.ml.20160205.12
Page(s) 36-41
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), 2016. Published by Science Publishing Group

Keywords

Chaos Synchronization, Complete Synchronization, Anti-synchronization, Hybrid Synchronization Nonlinear Dynamical Systems, Nonlinear Active Control

References
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Cite This Article
  • APA Style

    Maysoon M. Aziz, Saad Fawzi AL-Azzawi. (2016). Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems. Mathematics Letters, 2(5), 36-41. https://doi.org/10.11648/j.ml.20160205.12

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    ACS Style

    Maysoon M. Aziz; Saad Fawzi AL-Azzawi. Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems. Math. Lett. 2016, 2(5), 36-41. doi: 10.11648/j.ml.20160205.12

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    AMA Style

    Maysoon M. Aziz, Saad Fawzi AL-Azzawi. Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems. Math Lett. 2016;2(5):36-41. doi: 10.11648/j.ml.20160205.12

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  • @article{10.11648/j.ml.20160205.12,
      author = {Maysoon M. Aziz and Saad Fawzi AL-Azzawi},
      title = {Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems},
      journal = {Mathematics Letters},
      volume = {2},
      number = {5},
      pages = {36-41},
      doi = {10.11648/j.ml.20160205.12},
      url = {https://doi.org/10.11648/j.ml.20160205.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160205.12},
      abstract = {Three important phenomena of chaos synchronization are considered in this paper, In detailed, complete synchronization, anti- synchronization and hybrid synchronization based on the nonlinear active control approach between two different (non-identical) 4D hyperchaotic systems, i. e. Modified Pan and Liu are study herein. The Modified hyperchaotic Pan system is taken as drive system and hyperchaotic Liu system as response. Stabilization of error dynamics for each phenomenon is realized by satisfying two analytical approaches; Lyapunov's second method and linear system theory. Controllers are designed by using the relevant variable of drive and response systems. Theoretical analysis and numerical simulations are shown to verify the results.},
     year = {2016}
    }
    

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    T1  - Complete Synchronization, Anti-synchronization and Hybrid Synchronization Between Two Different 4D Nonlinear Dynamical Systems
    AU  - Maysoon M. Aziz
    AU  - Saad Fawzi AL-Azzawi
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    T2  - Mathematics Letters
    JF  - Mathematics Letters
    JO  - Mathematics Letters
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    UR  - https://doi.org/10.11648/j.ml.20160205.12
    AB  - Three important phenomena of chaos synchronization are considered in this paper, In detailed, complete synchronization, anti- synchronization and hybrid synchronization based on the nonlinear active control approach between two different (non-identical) 4D hyperchaotic systems, i. e. Modified Pan and Liu are study herein. The Modified hyperchaotic Pan system is taken as drive system and hyperchaotic Liu system as response. Stabilization of error dynamics for each phenomenon is realized by satisfying two analytical approaches; Lyapunov's second method and linear system theory. Controllers are designed by using the relevant variable of drive and response systems. Theoretical analysis and numerical simulations are shown to verify the results.
    VL  - 2
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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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