The Bifurcations of Completely Integrable Holonomic Systems of First-Order Differential Equations

As an application of the Legendrian singularity theory, we classify the bifurcations of a holonomic first-order differential equation with a complete integral. The equations satisfy that the one-parameter integral diagrams are R+-simple and stable. Using this result, the parametric differential equation models in electrical power systems and engineering can be studied.