Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator

This paper is concerned with numerical continuation and analytical investigations of sliding bifurcations in Filippov systems. In particular, a methodology developed for the continuation of grazing bifurcations in impacting systems is used to continue sliding bifurcations in Filippov systems. A dry-friction oscillator is investigated from a sliding bifurcations point of view and a complex two-parameter bifurcation diagram of sliding bifurcations is presented. A number of codimension-two sliding bifurcation points that act as organising centres for codimension-one sliding bifurcations are revealed. Two representative codimension-two points are analysed and unfolded, and the analysis is used to explain the dynamics of the dry-friction oscillator in the neighbourhood of these points.