Abstract
In this chapter, from Luo (2008a, 2008b, 2009, 2012a, 2012b), a general theory for the passability of a flow to a specific boundary in discontinuous dynamical systems will be reviewed. 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.
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References
Luo, A.C.J. 2005a. A Theory for Non-smooth Dynamic Systems on the Connectable Domains. Communications in Nonlinear Science and Numerical Simulation 10: 1–55.
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Luo, A.C.J., O’Connor, D.M. (2015). A General Theory for Flow Passability. In: System Dynamics with Interaction Discontinuity. Nonlinear Systems and Complexity, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-17422-8_3
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DOI: https://doi.org/10.1007/978-3-319-17422-8_3
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17421-1
Online ISBN: 978-3-319-17422-8
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