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Abstract
Using the singularity theory of scalar functions, we derive a classification of sliding bifurcations in piecewisesmooth flows. These are global bifurcations which occur when distinguished orbits become tangent to surfaces of discontinuity, called switching manifolds. The key idea of the paper is to attribute sliding bifurcations to singularities in the manifold’s projection along the flow, namely to points where the projection contains folds, cusps, and twofolds (saddles and bowls). From the possible local configurations of orbits we obtain sliding bifurcations.
In this way we derive a complete classification of generic oneparameter sliding bifurcations at a smooth codimension one switching manifold in ndimensions for n greater than 2. We uncover previously unknown sliding bifurcations, all of which are catastrophic in nature. We also describe how the method can be extended to sliding bifurcations of codimension two or higher.
Original language  English 

Pages (fromto)  505525 
Number of pages  21 
Journal  Siam Review 
Volume  53 
Issue number  3 
DOIs  
Publication status  Published  2011 
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Dive into the research topics of 'The geometry of generic sliding bifurcations'. Together they form a unique fingerprint.Projects
 1 Finished

CA Fellowship for Mike Jeffrey  When Worlds Collide: The Asymptotics of Interacting Systems
Jeffrey, M.
Engineering and Physical Sciences Research Council
1/08/11 → 31/07/12
Project: Research council