BIFURCATION FOR DYNAMICAL SYSTEMS OF PLANET–BELT INTERACTION

Abstract

The dynamical systems of planet–belt interaction are studied by the fixed-point analysis, and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of fixed points are determined by the parameters and these fixed points are either structurally stable or unstable. In addition to that, there are two special fixed points: The one on the inner edge of the belt is asymptotically stable and the one on the outer edge of the belt is unstable. This is consistent with the observational picture of Asteroid Belt between Mars and Jupiter: Mars moves steadily close to the inner edge but Jupiter is quite far from the outer edge.