On the Cusp Catastrophe Model and Stability

In this paper, we present results on the projection of the folding part of the cusp catastrophe model on the control space to find stability and catastrophic phenomenon of the periodic solutions of some nonlinear differential equations by using methods of catastrophe theory. We have shown here, that the occurrence of the folding of the cusp surface is always accompanied with the saddle - node bifurcation, and that the saddle - node bifurcation can be classified as cusp type catastrophe.