Homoclinic bifurcations in self-excited oscillators

This paper suggest an analytical criterion to predict saddle-loop bifurcations in single degree of freedom systems. The idea consists of computing explicitly an approximation of the self-excited periodic solution as well as its period. As a criterion of saddle-loop connection, the condition of vanishing of the frequency of this periodic solution is considered. This criterion can be used to predict the homoclinic connexion in three-dimensional systems, when the period of the periodic solution is performed.