Hysteresis suppression and synchronization near 3:1 subharmonic resonance

Effect of a high-frequency excitation on hysteresis and synchronization area in a forced van der Pol–Duffing oscillator near the subharmonic 3:1 resonance is analyzed. By means of perturbation techniques, the 3:1 resonance area and the quasiperiodic modulation domain are captured. The results shown that adding a high-frequency excitation causes the backbone curves to shift and to bend from softening to hardening. The results also reveal that a high-frequency excitation significantly affects the resonance and the synchronization zones. Further, jump phenomenon occurring in a certain range of the forcing frequency suggesting that hysteresis near the 3:1 subharmonic resonance cannot be ignored in practical applications.