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.
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