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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Mohammed Nokhas Murad Kaki, Department of Mathematics, Faculty of Science and Science Education, School of Science, Sulaimani University, Sulaimani, Iraq
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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.
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
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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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