Bifurcation analysis of a self-excited oscillator with different constraints by moving belt friction

This paper investigates theoretically conventional and non-smooth bifurcations of a self-excited oscilla-tor driven by moving belt friction under different constraint conditions. Firstly, theoretical conditions for the occurrence of various sliding bifurcations are established. Secondly, for each constraint, when equilibrium points are located in some region, their stability conditions and the existence criteria for both supercritical and subcritical Hopf bifurcations are derived, which demonstrates that for different constraints, the dynamical behaviors differ significantly. It is well known that there is little theoretical research on bifurcations in non-smooth systems and these research findings bridge the theoretical gaps in the analysis of non-smooth dynamical systems. The theoretical analysis is validated through numerical simulations, which confirms the presence of sliding bifurcations (crossing-sliding bifurcation, grazing-sliding bifurcation, switching-sliding bifurcation), as well as supercritical and subcritical Hopf bifurcations. Furthermore, we observe that a periodic orbit emerging from a supercritical Hopf bifurca-tion, upon further parameter variation, may begin to intersect the switching boundary, leading to various sliding bifurcations, which is different from the phenomenon described in previous references. A novel coexistence of subcritical Hopf bifurcation and crossing-sliding bifurcation, grazing-sliding bifurcation, or switching-sliding bifurcation is found through nemerical simelation, which is consistent with the theoretical analysis. It is noted that the phenomenon is rarely reported in prior studies and we discovered new bifurcation phenomenons. In a word, this study provides a refined theoretical framework for analyzing both sliding bifurcations and Hopf bifurcations in non-smooth dynamical systems with different constraints.