A theory for flow switchability in discontinuous dynamical systems |
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| Authors: | Albert CJ Luo |
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| Institution: | aDepartment of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL 62026-1805, USA |
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| Abstract: | The G-functions for discontinuous dynamical systems are introduced to investigate singularity in discontinuous dynamical systems. Based on the new G-function, the switchability of a flow from a domain to an adjacent one is discussed. Further, the full and half sink and source, non-passable flows to the separation boundary in discontinuous dynamical systems are discussed. A flow to the separation boundary in a discontinuous dynamical system can be passable or non-passable. Therefore, the switching bifurcations between the passable and non-passable flows are presented. Finally, the first integral quantity increment for discontinuous dynamical systems is given instead of the Melnikov function to develop the iterative mapping relations. |
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| Keywords: | Passable flow Non-passable flow Flow switching bifurcation Switchability First integral quantity increment Discontinuous dynamical systems Sliding bifurcation Sliding fragmentation Real flow Imaginary flow |
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