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

Abdellah Menasri

doi:doi:10.11648/j.pamj.20190802.12

| Peer-Reviewed

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

Abdellah Menasri

Published in Pure and Applied Mathematics Journal (Volume 8, Issue 2)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	Pure and Applied Mathematics Journal (Volume 8, Issue 2)
DOI	10.11648/j.pamj.20190802.12
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), 2019. Published by Science Publishing Group

Keywords

Dynamic Analysis, Nonlinear Continuous System, Three Dimensions

References

[1]	J. Lu, T. Zhou, G. Chen & S. Zhang, [2001] "Local bifurcations of the Chen system", International Journal of bifurcations and Chaos, 12, 2257-2270.
[2]	T. Zhou & G. Chen, [2006] "Classification of Chaos in 3-D Autonomous quadratic System-I", International Journal of Bifurcation and Chaos, 16, 2459--2479.
[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.
[5]	Paulo B. Gonçalves, Frederico M. A. Silva, Zenn J. G. N. Del Prado, [2016] Reduced order models for the nonlinear dynamic analysis of shells, 19, 118-125.
[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.
[8]	Huilan Yang, Huilan Yang, Huilan Yang, [2018] Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control, Applied Mathematics and Computation, 320, 75-85.
[9]	Liqiang Yao, Weihai Zhang, [2018] Stability analysis of random nonlinear systems with time-varying delay and its application, Journal of latex classe files.
[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.
[11]	Màrio Bessa, Jorge Rocha, Paulo Varandas, [2018] Uniform hyperbolicity revisited: index of periodic points and equidimensional cycles, Journal dynamical systems, 33, 4.
[12]	Stephen Baigent, Zhanyuan Hou, [2017] Global stability of discrete-time competitive population models, Journal of Difference Equations and Applications, 23, 8.
[13]	S. O. Papkov, [2016] Three-Dimensional Dynamic Problem of the Theory of Elasticity for a Parallelepiped, Journal of Mathematical Sciences, 215, 2, 121-142.
[14]	Xianmai Chen, Xiangyun Deng, Lei Xu, [2018] A Three-Dimensional Dynamic Model for Railway Vehicle--Track Interactions, Journal of Computational and Nonlinear Dynamics, 13, 7, 1-10.
[15]	Xinghua Fan, Ying Zhang, Jiuli Yin, [2018] Evolutionary Analysis of a Three-Dimensional Carbon Price Dynamic System, Sustainability, 11, 1.

Cite This Article

Plain Text BibTeX RIS

APA Style

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

Copy | Download

ACS 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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Dynamic Analysis of a Three-dimensional Non-linear Continuous System
AU  - Abdellah Menasri
Y1  - 2019/07/10
PY  - 2019
N1  - https://doi.org/10.11648/j.pamj.20190802.12
DO  - 10.11648/j.pamj.20190802.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 37
EP  - 46
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20190802.12
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.
VL  - 8
IS  - 2
ER  -

Copy | Download

Author Information

Abdellah Menasri

Department of Process Engineering, University of Constantine 3, Constantine, Algeria

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

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

Copy | Download

ACS 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

Copy | Download

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Dynamic Analysis of a Three-dimensional Non-linear Continuous System
AU  - Abdellah Menasri
Y1  - 2019/07/10
PY  - 2019
N1  - https://doi.org/10.11648/j.pamj.20190802.12
DO  - 10.11648/j.pamj.20190802.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 37
EP  - 46
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20190802.12
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.
VL  - 8
IS  - 2
ER  -

Copy | Download