Nonstandard bifurcations in oscillators with multiple discontinuity boundaries

The model of a double-belt friction oscillator is proposed, which exhibits multiple discontinuity boundaries in the phase space. The system consists of a simple oscillator dragged by two different rough supports moving with constant driving velocities and subjected to an elastic restoring force and viscous damping. Self-sustained oscillations have been observed to occur, with nonstandard attracting properties. By considering the problem from a nonsmooth dynamical systems perspective, the evolution of steady state attractors as the velocities of the belts are varied is described. The nonsmoothness sets of the system at hand and, in particular, the presence of multiple discontinuity boundaries, lead to nonstandard bifurcations which are studied here by means of analytical and numerical tools.