On flow switching bifurcations in discontinuous dynamical systems. (English) Zbl 1102.37014

Summary: The sliding dynamics on the separation boundary is discussed based on the set-valued vector field theory. From vector fields in the neighborhood of a specific separation boundary, the passability of the flow from the one domain into another one is further discussed. The switching bifurcation conditions from the passable boundary to the non-passable boundary are developed. The sliding flow fragmentation on the separation boundary surface is also presented. The normal vector product field function is introduced to determine the switching bifurcation and sliding fragmentation.


37C10 Dynamics induced by flows and semiflows
34A36 Discontinuous ordinary differential equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
34C23 Bifurcation theory for ordinary differential equations
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