The Asymmetric Periodically Forced Van Der Pol Oscillator (European Journal of Pure and Applied Mathematics, 2025)
We review geometric singular perturbation theory (GSPT) which has been used to explain the behaviour of the singular slow-fast system near the singular limit. In particular, we follow the analysis of Guckenheimer et al. [1] for the periodically forced symmetric van der Pol oscillator (β = 0), then we constructed the Poincare return map for studying the bifurcation phenomena of this model. We ´ generalise to a asymmetric forced van der Pol oscillator for β , 0. We show that the forced asymmetric van der Pol oscillator can become frequency locked due to the forcing. Then, we extend this analysis to show how the symmetry breaking parameter β in a periodically forced van der Pol oscillator influences the width of Arnold tongues (also known as frequency locking regions), and we find these frequency locking regions in the parameter space (a, ω).
Keywords: Slow-fast systems; Dynamical Systems; Bifurcation analysis