Abstract
In this chapter, from (2008a, 2008b), a theory of flow switchability to the boundary in discontinuous dynamical systems will be presented. The G-functions for discontinuous dynamical systems will be introduced to investigate singularity in discontinuous dynamical systems. Based on the G-functions, the full and half sink and source, non-passable flows to the separation boundary in the systems will be presented, and the switchability of a flow from a domain to an adjacent one will also be discussed. Therefore, the switching bifurcations between the passable and non-passable flows will be presented. The basic theory will be applied to determine the complexity in the systems with time-varying domains in Chapters 4∼6.
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References
Luo, A. C. J. (2005a). A theory for nonsmooth dynamic systems on the connectable domains, Communications in Nonlinear Science and Numerical Simulation, 10, pp. 1–55.
Luo, A. C. J. (2005b), Imaginary, sink and source flows in the vicinity of separatrix of non-smooth dynamical systems, Journal of Sound and Vibration, 285, pp. 443–456.
Luo, A. C. J. (2006), Singularity and Dynamics on Discontinuous Vector Fields. Amsterdam: Elsevier.
Luo, A. C. J. (2007a), A theory for n-dimensional, nonlinear dynamics on continuous vectorfields. Communications in Nonlinear Science and Numerical Simulation, 12, pp. 117–194.
Luo, A. C. J. (2007b), On flow switching bifurcations in discontinuous dynamical systems, Communications in Nonlinear Science and Numerical Simulation, 12, pp. 100–116.
Luo, A. C. J. (2008a), A theory for flow switchability in discontinuous dynamical systems, Nonlinear Analysis: Hybrid Systems, 2(4), pp. 1030–1061.
Luo, A. C. J. (2008b) Global Transversality. Resonance and Chaotic Dynamics, Singapore: World Scientific.
Luo, A. C. J. (2008c). On the differential geometry of flows in nonlinear dynamic systems, ASME Journal of Computational and Nonlinear Dynamics, 021104–1-10.
Luo, A. C. J. (2008d), Global tangency and transversality of periodic flows and chaos in a periodically forced, damped Duffing oscillator, International Journal of Bifurcations and Chaos, 18, pp. 1–49.
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© 2009 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg
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(2009). Flow Switchability. In: Discontinuous Dynamical Systems on Time-varying Domains. Nonlinear Physical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00253-3_2
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DOI: https://doi.org/10.1007/978-3-642-00253-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00252-6
Online ISBN: 978-3-642-00253-3
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