Gauge Function as a New and Powerful Tool to Study the Van der Pol Oscillator

A gauge function for the van der Pol oscillator is constructed and used to perform stability analysis of this system as well as to determine its dynamical states without solving the corresponding equation of motion. Despite previous claims that the oscillator is a non-Lagrangian system, it is shown that the gauge function allows deriving its first Lagrangian. The presented results demonstrate that the gauge function is a new and powerful tool to study this system and that it gives deeper physical insights into the system’s nature than any tool previously used.