Georgia Institute of Technology College of Sciences

We consider several possibilities on how to select a Filippov sliding vector field on a co-dimension 2 singularity manifold, intersection of two co-dimension 1 manifolds, under the assumption of general attractivity. Of specific interest is the selection of a smoothly varying Filippov sliding vector field. As a result of our analysis and experiments, the best candidates of the many possibilities explored are based on the so-called barycentric coordinates: in particular, we choose what we call the moments solution. We then examine the behavior of the moments vector field at first order exit points, and show that it aligns smoothly with the exit vector field. Numerical experiments illustrate our results and contrast the present method with other choices of Filippov sliding vector field. We further present some minimum variation properties, related to orbital equivalence, of Filippov solutions for the co-dimension 2 case in \R^{3}.