  In this Letter we explore the possibility of a supercritical Hopf bifurcation
in a typical parametric nonlinear oscillator which has been excited by two
frequencies, one slow and the other fast, through the variation of the
frequency of the rapidly oscillating driving force. Studies of nonlinear
responses and bifurcations of such driven nonlinear systems are usually done by
treating the strength of the fast drive as the control parameter. Here we show
that, beyond its role in allowing one to study the dynamics with the slow and
fast components nicely separated, the fast frequency can also be used as an
independent control parameter for studying Hopf bifurcation.
