Pure and Applied Mathematics Journal

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Dynamic Analysis of a Three-dimensional Non-linear Continuous System

Received: 18 December 2018    Accepted: 19 March 2019    Published: 10 July 2019
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Abstract

Most physical phenomena are modeled as continuous or discrete dynamic systems of a second dimension or more, but because of the multiplicity of bifurcation parameters and the large dimension, researchers have big problems for the study of this type of systems. For this reason, this article proposes a new method that facilitates the qualitative study of continuous dynamic systems of three dimensions in general and chaotic systems in particular, which contains many parameters of bifurcations. This method is based on projection on the plane and on an appropriate bifurcation parameter.

DOI 10.11648/j.pamj.20190802.12
Published in Pure and Applied Mathematics Journal (Volume 8, Issue 2, April 2019)
Page(s) 37-46
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), 2024. Published by Science Publishing Group

Keywords

Dynamic Analysis, Nonlinear Continuous System, Three Dimensions

References
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[3] S. Dadras, H. Re. Momeni & Qi. Guoyuan, [2007] "Analysis of a new 3-D smooth autonomous system with different wing chaotic attractors and transient chaos", Indian Journal of Microbiology, 62, 391-405.
[4] B. K. Maheshwari, K. Z. Truman, [2004] 3-D finite element nonlinear dynamic analysis for soil-pile-structure interaction, 13th World Conference on Earthquake Engineering Vancouver, B. C., Canada, 1570.
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[6] Dejan Zupan, [2018] Dynamic analysis of geometrically non-linear three-dimensional beams under moving mass, Journal of Sound and Vibration, 413, 354-367.
[7] Jihua Dong, [2016] A dynamic systems theory approach to development of listening strategy use and listening performance, Elsevier, 63, 149-165.
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[10] Marwen Kermani, Anis Sakly, [2019] On Robust Stability Analysis of Uncertain Discrete-Time Switched Nonlinear Systems with Time Varying Delays, Mathematical Problems in Engineering, 2018, 14.
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Author Information
  • Department of Process Engineering, University of Constantine 3, Constantine, Algeria

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    Abdellah Menasri. (2019). Dynamic Analysis of a Three-dimensional Non-linear Continuous System. Pure and Applied Mathematics Journal, 8(2), 37-46. https://doi.org/10.11648/j.pamj.20190802.12

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    Abdellah Menasri. Dynamic Analysis of a Three-dimensional Non-linear Continuous System. Pure Appl. Math. J. 2019, 8(2), 37-46. doi: 10.11648/j.pamj.20190802.12

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    AMA Style

    Abdellah Menasri. Dynamic Analysis of a Three-dimensional Non-linear Continuous System. Pure Appl Math J. 2019;8(2):37-46. doi: 10.11648/j.pamj.20190802.12

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  • @article{10.11648/j.pamj.20190802.12,
      author = {Abdellah Menasri},
      title = {Dynamic Analysis of a Three-dimensional Non-linear Continuous System},
      journal = {Pure and Applied Mathematics Journal},
      volume = {8},
      number = {2},
      pages = {37-46},
      doi = {10.11648/j.pamj.20190802.12},
      url = {https://doi.org/10.11648/j.pamj.20190802.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20190802.12},
      abstract = {Most physical phenomena are modeled as continuous or discrete dynamic systems of a second dimension or more, but because of the multiplicity of bifurcation parameters and the large dimension, researchers have big problems for the study of this type of systems. For this reason, this article proposes a new method that facilitates the qualitative study of continuous dynamic systems of three dimensions in general and chaotic systems in particular, which contains many parameters of bifurcations. This method is based on projection on the plane and on an appropriate bifurcation parameter.},
     year = {2019}
    }
    

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    AB  - Most physical phenomena are modeled as continuous or discrete dynamic systems of a second dimension or more, but because of the multiplicity of bifurcation parameters and the large dimension, researchers have big problems for the study of this type of systems. For this reason, this article proposes a new method that facilitates the qualitative study of continuous dynamic systems of three dimensions in general and chaotic systems in particular, which contains many parameters of bifurcations. This method is based on projection on the plane and on an appropriate bifurcation parameter.
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