PERSISTENCE OF THE SADDLE-NODE BIFURCATION FOR NONLINEAR-SYSTEMS WITHSLOW UNMODELED DYNAMICS

This paper investigates the robustness of the saddle-node bifurcation for nonlinear systems under the addition of slow unmodeled dynamics. T he robustness is examined in terms of existence and system behavior af ter bifurcation. Under fairly general conditions, it is shown that if the reduced model of a physical system encounters a saddle-node bifurc ation due to a varying parameter, then the original model which includ es small unmodeled dynamics will also encounter a saddle-node bifurcat ion. An error bound is derived between the bifurcation values and the bifurcation points of the reduced model and that of the original model . Furthermore, it is shown that the dynamics after the saddle-node bif urcation of the reduced model and that of the original model are appro ximately the same. The persistence and non-persistence of saddle-node bifurcations are illustrated by several examples.