Bursting oscillations of the perturbed quasi-zero stiffness system with positive/negative stiffness at origin

In this paper, we investigate the bursting oscillations of a system with positive or negative stiffness at origin perturbed by the QZS system. The complex global dynamics are studied by the bifurcation analysis of the generalized autonomous system in which the low-frequency excitation is treated as a slow-varying parameter. The patterns of bursting oscillations and its mechanisms are revealed for the cases of single-well dynamics, double-well dynamics, critical and transition between both. There are three types of bursting oscillations appeared in both the double-well dynamics and the critical dynamics except the single-well one, two of them are asymmetric and the other is symmetric. It is also found that the condition of the asymmetric bursting oscillations occurred in the critical dynamics is a small limit cycle near the fold point. A novel fish-scale curve is found under transition dynamics and the analysis shows that the flaking phenomenon of fish-scale corresponds to the reduction of peak number in bursting oscillations, which is caused by the adaptability of system when slow-varying parameter changes more faster with the increasing excitation amplitude.