The Non-Autonomous Saddle Node Bifurcation

Abstract

This work explores the phenomenon of saddle-node bifurcation in both autonomous and non-autonomous dynamical systems. The classical autonomous case is illustrated through a simple differential equation that demonstrates the creation and annihilation of fixed points as a system parameter varies. The focus then shifts to the more complex non-autonomous case, where the system's behavior depends explicitly on time. It is shown that, under certain conditions, a similar bifurcation occurs even without time-invariant dynamics.