Jeffrey, M. R. and Colombo, A., 2009. The two-fold singularity of discontinuous vector fields. SIAM Journal on Applied Dynamical Systems, 8 (2), pp. 624-640.
When a vector field in three dimensions is discontinuous on a smooth codimension one surface, it may be simultaneously tangent to both sides of the surface at generic isolated points (singularities). For a piecewise-smooth dynamical system governed by the vector field, we show that the local dynamics depends on a single quantity—the jump in direction of the vector field through the singularity. This quantity controls a bifurcation, in which the initially repelling singularity becomes the apex of a pair of parabolic invariant surfaces. The surfaces are smooth except where they intersect the discontinuity surface, and they divide local space into regions of attraction to, and repulsion from, the singularity.
|Item Type ||Articles|
|Creators||Jeffrey, M. R.and Colombo, A.|
|Departments||Faculty of Science > Mathematical Sciences|
|Publisher Statement||2009SIADS_2fold.pdf: ©SIAM|
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