Analysis of a quasiperiodically forced van der Pol oscillator using geometric singular perturbation theory

This paper is motivated by study of long timescale variability of the climate system. We focus on a model of nonlinear behaviour that is used in climate modelling. This is the forced van der Pol oscillator, motivated by examination of the Pleistocene ice age oscillations forced by astronomical orbital variations. We discuss a forced van der Pol oscillator, following the analysis of Guckenheimer et al. for periodically cases. We use a geometric singular perturbation theory (GSPT) approach of Guckenheimer et al. to reduce to the dynamics of the return map and extend to their work to construct return maps for quasiperiodically forced cases. We note this return map can be noninvertible in various values to the parameters.