Discontinuity and Local Singularity
In this chapter, a general theory for the passability of a flow to a specific boundary in discontinuous dynamical systems will be discussed. The concepts of real and imaginary flows will be introduced. The G-functions for discontinuous dynamical systems will be presented to describe the passability of a flow to the boundary. Based on the G-function, the passability of a flow from a domain to an adjacent one will be discussed. With the concepts of real and imaginary flows, the full- and half-sink and source flows to the boundary will be discussed as well. A flow to the boundary in a discontinuous dynamical system can be passable or non-passable. Thus, all possible switching bifurcations between the passable and non-passable flows will be presented.