Saddle-Node Bifurcation

A saddle-node bifurcation is a concept in dynamical systems where, as a parameter changes, two equilibrium points—one stable and one unstable—move toward each other and eventually merge into a single point. Beyond this critical change, both equilibria disappear. This process can cause sudden shifts or transitions in a system's behavior, like abruptly switching from one state to another. It helps explain phenomena in various fields, such as physics, biology, and economics, where gradual changes in conditions can lead to rapid, qualitative transformations in system dynamics.