Singularity and Flow Passability

Albert C. J. Luo ()
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Albert C. J. Luo: Southern Illinois University Edwardsville, Department of Mechanical and Industrial Engineering

Chapter Chapter 3 in Discontinuous Dynamical Systems, 2012, pp 77-164 from Springer

Abstract: Abstract In this chapter, a general theory for the passability of a flow to a specific boundary in discontinuous dynamical systems will be presented. The concepts of real and imaginary flows will be introduced. The G-functions for discontinuous dynamical systems will be developed to describe the general theory of 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 in detail. A flow to the boundary in a discontinuous dynamical system can be passable or non-passable. Thus, all the switching bifurcations between the passable and non-passable flows will be presented. To understand the concept of flow passability, a discontinuous dynamical system with a parabolic boundary is presented as an example.

Keywords: Vector Field; Tangential Vector; Periodic Motion; Real Flow; Parabolic Boundary (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-22461-4_3

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DOI: 10.1007/978-3-642-22461-4_3

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