On the Butterfly Catastrophe Model and Stability of Finite Periodic Solutions for Some Non-Linear Differential Equations

In this work, we find the results for the folded part projection of the butterfly catastrophe model onto the control space, using methods from catastrophe theory to obtain stability and the catastrophic behavior of finite periodic solutions for some non-linear differential equations. Finally, we have shown that a saddle-node bifurcation, which can be classified as a butterfly mutation, accompanies butterfly surface folding.