Turnover of hysteresis determines novel bursting in Duffing system with multiple-frequency external forcings

This paper investigates bursting dynamics of the Duffing system with multiple-frequency external forcings, in which novel bursting patterns (i.e., the so-called turnover-of-hysteresis-induced bursting patterns) can be observed. Typically, distinct oscillations are observed in the quasi-static processes of these bursting patterns. We show that the oscillations appear in the quasi-static processes because the equilibrium hysteresis curve of the fast subsystem becomes the one with twists and turns, and this forms a new route to bursting, which we call turnover of hysteresis. Besides, we investigate the effects of forcing frequencies and amplitudes on the turnover-of hysteresis-induced bursting. Our study shows that the three frequency components observed in the bursting are decided by the forcing frequencies, while the transition of the bursting depends on the forcing amplitudes.