Ⅰ.OBJECTIVE OF THE RESEARCH Being a commonly observed phenomenon in switched dynamical systems,border collision has attracted much attention in recent years.Like other typical bifurcation scenarios,border collision (BC) manifests itself as a sudden change of qualitative behavior of a system as one or more parameters are varied,and hence can be regarded as a kind of bifurcation phenomenon.However,BC has always been considered separately from such traditional bifurcations.This can be attributed to the fundamental difference in the mechanisms underlying BC and traditional bifurcations.Specifically,traditional bifurcations are caused by a loss of stability of an operating orbit and the assumption of a new stable orbit,whereas BC is resulted from operational change in which an operating orbit fails to maintain itself due to some inherent structural property of the system [1].The system thus typically jumps to another stable operating orbit at border collision.Moreover,no loss of stability is required for BC.Up to now,because of the apparent lack of commonality between border collision and traditional bifurcations,no connection has been known that links the two types of coexisting bifurcations in a given switched dynamical system.