BIFURCATIONS IN IMPACT OSCILLATIONS

Models of impact oscillators using an instantaneous impact law are by their very nature discontinuous. These discontinuities give rise to bi furcations which cannot be classified using the usual tools of bifurca tion analysis. However, we present numerical evidence which suggests t hat these discontinuous bifurcations are just the limits (in some sens e) of standard bifurcations of smooth dynamical systems as the impact is hardened. Finally we show how one dimensional maps of the interval with essentially similar characteristics can exhibit the same kinds of bifurcational behaviour, and how these bifurcations are related to st andard bifurcations.