Horseshoes of periodically kicked van der Pol oscillators

This paper contains a numerical study of the periodically forced van der Pol system. Our aim is to determine the extent to which chaotic behavior occurs in this system as well as the nature of the chaos. Unlike previous studies, which used continuous forcing, we work with instantaneous kicks, for which the geometry is simpler. Our study covers a range of parameters describing nonlinearity, kick sizes, kick periods. We show that horseshoes are abundant whenever the limit cycle is kicked to a specific region of the phase space offer a geometric explanation for the stretch-and-fold behavior which ensues.