Notions of Attractivity and Bifurcation

In this chapter, new concepts of (local) attractivity and repulsivity (in Section 2.3) and bifurcation and transition (in Section 2.5) are introduced for nonautonomous dynamical systems. By a bifurcation and transition, a qualitative change of attractivity or repulsivity is meant. Due to the nonautonomous framework, it is distinguished between four distinct points of view concerning di.erent time domains. The notions of attractivity and repulsivity—and for this reason also the notions of bifurcation and transition—are introduced for the past (past attractivity and repulsivity), the future (future attractivity and repulsivity), the entire time (all-time attractivity and repulsivity) and the present (finite-time attractivity and repulsivity) of the system.