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The two-fold singularity of discontinuous vector fields


Reference:

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.

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    Official URL:

    http://dx.doi.org/10.1137/08073113X

    Abstract

    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.

    Details

    Item Type Articles
    CreatorsJeffrey, M. R.and Colombo, A.
    DOI10.1137/08073113X
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher Statement2009SIADS_2fold.pdf: ©SIAM
    RefereedYes
    StatusPublished
    ID Code26964

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