SAFE, EXPLOSIVE, AND DANGEROUS BIFURCATIONS IN DISSIPATIVE DYNAMICAL-SYSTEMS

A comprehensive listing of the generic codimension-1 attractor bifurcations of dissipative dynamical systems is presented. It includes local and global bifurcations of regular and chaotic attractors. The bifurcations are classified according to the continuity or discontinuity of the attractor path, which governs the physical outcome that would be observed under a slow control sweep. Related issues of determinacy, hysteresis, basin structure, and intermittency are addressed. Recently discovered chaotic bifurcations are discussed in some detail, with particular reference to the regular or chaotic saddle-type destroyer with which an attractor may collide.