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

Hopf Bifurcation in vibrational resonance through modulation of fast frequency