Degenerate Grazing Bifurcations in a Simple Bilinear Oscillator

Degenerate grazing bifurcation occurring in a simple bilinear oscillator, namely the limit discontinuous case of the smooth and discontinuous (SD) oscillator, is investigated by numerical simulations. The unperturbed system has a saddle-like singularity at the origin with two periodic orbits grazing at the same point. The matrix in the leading-order truncation of the Poincaré map at a grazing bifurcation for either of the two periodic orbits has...