The Stability and Catastrophic Behavior of Finite Periodic Solutions in Non-Linear Differential Equations

Abstract

This study focuses on the stability and catastrophic behavior of finite periodic solutions in non-linear differential equations. The occurrence of folding surfaces and their relationship with saddle-node bifurcations are explored, being classified as fold and butterfly types of catastrophes. Additionally, the application of catastrophe theory is discussed to analyze the qualitative changes in solutions with the change in system parameters.