Krylov Bogoliubov Type Analysis of Variants of the Mathieu Equation - Shayak, B.; Vyas, Pranav (Journal of Applied Nonlinear Dynamics, 2026)
In this work we show that a Krylov-Bogoliubov type analysis is a powerful method for analysing variants of the Mathieu equation. We first demonstrate the technique by rederiving the results obtained by prior authors using different techniques and then apply it to a case where the system has a quasiperiodic drive (inhomogeneity) in addition to a quasiperiodic parametric term. A realistic system where such a forcing is present is an induction motor, so we adopt that as our model system to show the details of the method.