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Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations

Received: 7 March 2017     Accepted: 8 March 2017     Published: 5 April 2017
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Abstract

Novel equi-attractivity in large generalized non-linear partial differential equations were performed for the impulsive control of spatiotemporal chaotic. Attractive solutions of these general partial differential equations were determined. A proof for existence of a certain kind of impulses for synchronization such that the small error dynamics that is equi-attractive in the large is established. A comparative study between these general non-linear partial differential equations and the existent reported numerical theoretical models was developed. Several boundary conditions were given to confirm the theoretical results of the general non-linear partial differential equations. Moreover, the equations were applied to Kuramoto–Sivashinsky PDE′s equation; Grey–Scott models, and Lyapunov exponents for stabilization of the large chaotic systems with elimination of the dynamic error.

Published in American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5-1)

This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics

DOI 10.11648/j.ajtas.s.2017060501.15
Page(s) 30-39
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

Synchronization, Impulsive Control, Prabolic Partial Differential Equations

References
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  • APA Style

    Mahmoud M. El-Borai, Wagdy G. Elsayed, Turkiya Alhadi Aljamal. (2017). Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations. American Journal of Theoretical and Applied Statistics, 6(5-1), 30-39. https://doi.org/10.11648/j.ajtas.s.2017060501.15

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    ACS Style

    Mahmoud M. El-Borai; Wagdy G. Elsayed; Turkiya Alhadi Aljamal. Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations. Am. J. Theor. Appl. Stat. 2017, 6(5-1), 30-39. doi: 10.11648/j.ajtas.s.2017060501.15

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    AMA Style

    Mahmoud M. El-Borai, Wagdy G. Elsayed, Turkiya Alhadi Aljamal. Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations. Am J Theor Appl Stat. 2017;6(5-1):30-39. doi: 10.11648/j.ajtas.s.2017060501.15

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  • @article{10.11648/j.ajtas.s.2017060501.15,
      author = {Mahmoud M. El-Borai and Wagdy G. Elsayed and Turkiya Alhadi Aljamal},
      title = {Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {6},
      number = {5-1},
      pages = {30-39},
      doi = {10.11648/j.ajtas.s.2017060501.15},
      url = {https://doi.org/10.11648/j.ajtas.s.2017060501.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2017060501.15},
      abstract = {Novel equi-attractivity in large generalized non-linear partial differential equations were performed for the impulsive control of spatiotemporal chaotic. Attractive solutions of these general partial differential equations were determined. A proof for existence of a certain kind of impulses for synchronization such that the small error dynamics that is equi-attractive in the large is established. A comparative study between these general non-linear partial differential equations and the existent reported numerical theoretical models was developed. Several boundary conditions were given to confirm the theoretical results of the general non-linear partial differential equations. Moreover, the equations were applied to Kuramoto–Sivashinsky PDE′s equation; Grey–Scott models, and Lyapunov exponents for stabilization of the large chaotic systems with elimination of the dynamic error.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Synchronization and Impulsive Control of Some Parabolic Partial Differential Equations
    AU  - Mahmoud M. El-Borai
    AU  - Wagdy G. Elsayed
    AU  - Turkiya Alhadi Aljamal
    Y1  - 2017/04/05
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ajtas.s.2017060501.15
    DO  - 10.11648/j.ajtas.s.2017060501.15
    T2  - American Journal of Theoretical and Applied Statistics
    JF  - American Journal of Theoretical and Applied Statistics
    JO  - American Journal of Theoretical and Applied Statistics
    SP  - 30
    EP  - 39
    PB  - Science Publishing Group
    SN  - 2326-9006
    UR  - https://doi.org/10.11648/j.ajtas.s.2017060501.15
    AB  - Novel equi-attractivity in large generalized non-linear partial differential equations were performed for the impulsive control of spatiotemporal chaotic. Attractive solutions of these general partial differential equations were determined. A proof for existence of a certain kind of impulses for synchronization such that the small error dynamics that is equi-attractive in the large is established. A comparative study between these general non-linear partial differential equations and the existent reported numerical theoretical models was developed. Several boundary conditions were given to confirm the theoretical results of the general non-linear partial differential equations. Moreover, the equations were applied to Kuramoto–Sivashinsky PDE′s equation; Grey–Scott models, and Lyapunov exponents for stabilization of the large chaotic systems with elimination of the dynamic error.
    VL  - 6
    IS  - 5-1
    ER  - 

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Author Information
  • Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt

  • Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt

  • Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt

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