Horseshoes of Periodically-kicked van der Pol Oscillators
This talk will focus on a numerical study of the periodically forced van
der Pol system. The 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 and kick periods.
We show that horseshoes are abundant whenever the limit cycle is kicked to
a specific region of the phase space, and offer a geometric explanation
for the stretch-and-fold behavior which ensues.