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

Maysoon M. Aziz; Saad Fawzi Al-Azzawi

doi:doi:10.11648/j.ijtam.20170301.16

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

Maysoon M. Aziz, Saad Fawzi Al-Azzawi

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 1)

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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[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.
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[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.
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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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TY  - JOUR
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
Y1  - 2017/01/12
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170301.16
DO  - 10.11648/j.ijtam.20170301.16
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 36
EP  - 42
PB  - Science Publishing Group
SN  - 2575-5080
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

Maysoon M. Aziz

Department of Mathematics, College of Computer Sciences and Mathematics, University of Mosul, Mosul, Iraq
Saad Fawzi Al-Azzawi

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

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
Y1  - 2017/01/12
PY  - 2017
N1  - https://doi.org/10.11648/j.ijtam.20170301.16
DO  - 10.11648/j.ijtam.20170301.16
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 36
EP  - 42
PB  - Science Publishing Group
SN  - 2575-5080
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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