Catastrophic Types Depending on Degree of Non-Linearity
Pure and Applied Mathematics Journal
Volume 3, Issue 6-1, December 2014, Pages: 24-27
Received: Dec. 2, 2014; Accepted: Dec. 26, 2014; Published: Dec. 27, 2014
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Author
Mohammed Nokhas Murad Kaki, Department of Mathematics, Faculty of Science and Science Education, School of Science, Sulaimani University, Sulaimani, Iraq
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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.
Keywords
Cusp, Butterfly Catastrophe, Mathematical Model, Stability of Periodic Solution, Bifurcation
To cite this article
Mohammed Nokhas Murad Kaki, Catastrophic Types Depending on Degree of Non-Linearity, Pure and Applied Mathematics Journal. Special Issue: Mathematical Theory and Modeling. Vol. 3, No. 6-1, 2014, pp. 24-27. doi: 10.11648/j.pamj.s.2014030601.15
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.
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