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), 2024. Published by Science Publishing Group |
Cusp, Butterfly Catastrophe, Mathematical Model, Stability of Periodic Solution, Bifurcation
| [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. |
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
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
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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}
}
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 -
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