| Peer-Reviewed

Catastrophic Types Depending on Degree of Non-Linearity

Received: 2 December 2014     Accepted: 26 December 2014     Published: 27 December 2014
Views:       Downloads:
Abstract

In this paper, we present results on the projection of the folding part of the elementary catastrophe models on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations (NLDE) by using methods of catastrophe theory. We have shown here, that the cusp and Butterfly types depend on the degree of nonlinear differential equations, and that the bifurcation can be classified as cusp or butterfly types catastrophe. Moreover, our aim, in this work, is to obtain periodic solutions of some nonlinear differential equation (NLDE) and to study the stability of these periodic solutions and the main result is the following proposition: The catastrophic Types depending on the degree of non-linear differential equation.

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 6-1)

This article belongs to the Special Issue Mathematical Theory and Modeling

DOI 10.11648/j.pamj.s.2014030601.15
Page(s) 24-27
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), 2014. Published by Science Publishing Group

Keywords

Cusp, Butterfly Catastrophe, Mathematical Model, Stability of Periodic Solution, Bifurcation

References
[1] A. Mehdi, L. Jafsr, Solution of Nonlinear Oscillators Using Glubal Error, Adv. Studies Theor. Phys. Vol. 5, 2011, no. 8, 349-356
[2] Zeeman, C., Catastrophe Theory, Addison Wesley, (1977).
[3] Mohammad Nokhas Murad Kaki, Treatment of phenomena of instability by methods of catastrophe theory. M.Sc. Thesis, university of Baghdad, Baghdad, Iraq, (1985).
[4] Murad Mohammed Nokhas Kaki, On the Cusp Catastrophe Model and Stability, General Mathematics Notes(GMN),Vol. 2 No. 2, February, (2011).
[5] Mohammed Nokhas Murad Kaki, On the Catastrophic model and Stability, International Journal of Basic & Applied Science IJBAS-IJENS Vol. 12 No. 03 (2012) pp. 64- 67
[6] Murad Mohammed Nokhas Kaki, Salahaddin A. Aziz Stability and Existence of Periodic Solutions in Non-linear Differential Equations. International Journal of Emerging Technology and Advanced Engineering. Volume 3, Issue 6, (2013) pp. 574-577.
Cite This Article
  • APA Style

    Mohammed Nokhas Murad Kaki. (2014). Catastrophic Types Depending on Degree of Non-Linearity. Pure and Applied Mathematics Journal, 3(6-1), 24-27. https://doi.org/10.11648/j.pamj.s.2014030601.15

    Copy | Download

    ACS Style

    Mohammed Nokhas Murad Kaki. Catastrophic Types Depending on Degree of Non-Linearity. Pure Appl. Math. J. 2014, 3(6-1), 24-27. doi: 10.11648/j.pamj.s.2014030601.15

    Copy | Download

    AMA Style

    Mohammed Nokhas Murad Kaki. Catastrophic Types Depending on Degree of Non-Linearity. Pure Appl Math J. 2014;3(6-1):24-27. doi: 10.11648/j.pamj.s.2014030601.15

    Copy | Download

  • @article{10.11648/j.pamj.s.2014030601.15,
      author = {Mohammed Nokhas Murad Kaki},
      title = {Catastrophic Types Depending on Degree of Non-Linearity},
      journal = {Pure and Applied Mathematics Journal},
      volume = {3},
      number = {6-1},
      pages = {24-27},
      doi = {10.11648/j.pamj.s.2014030601.15},
      url = {https://doi.org/10.11648/j.pamj.s.2014030601.15},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.s.2014030601.15},
      abstract = {In this paper, we present results on the projection of the folding part of the elementary catastrophe models on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations (NLDE) by using methods of catastrophe theory. We have shown here, that the cusp and Butterfly types depend on the degree of nonlinear differential equations, and that the bifurcation can be classified as cusp or butterfly types catastrophe. Moreover, our aim, in this work, is to obtain periodic solutions of some nonlinear differential equation (NLDE) and to study the stability of these periodic solutions and the main result is the following proposition: The catastrophic Types depending on the degree of non-linear differential equation.},
     year = {2014}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Catastrophic Types Depending on Degree of Non-Linearity
    AU  - Mohammed Nokhas Murad Kaki
    Y1  - 2014/12/27
    PY  - 2014
    N1  - https://doi.org/10.11648/j.pamj.s.2014030601.15
    DO  - 10.11648/j.pamj.s.2014030601.15
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 24
    EP  - 27
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.s.2014030601.15
    AB  - In this paper, we present results on the projection of the folding part of the elementary catastrophe models on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations (NLDE) by using methods of catastrophe theory. We have shown here, that the cusp and Butterfly types depend on the degree of nonlinear differential equations, and that the bifurcation can be classified as cusp or butterfly types catastrophe. Moreover, our aim, in this work, is to obtain periodic solutions of some nonlinear differential equation (NLDE) and to study the stability of these periodic solutions and the main result is the following proposition: The catastrophic Types depending on the degree of non-linear differential equation.
    VL  - 3
    IS  - 6-1
    ER  - 

    Copy | Download

Author Information
  • Department of Mathematics, Faculty of Science and Science Education, School of Science, Sulaimani University, Sulaimani, Iraq

  • Sections