Bifurcations of dynamical systems with sliding: derivation of normal-form mappings

By Mario di Bernardo, Piotr Kowalczyk, A. Nordmark. 2002

252 citations recorded by the source corpus.

Subfields: Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d027c7fed7ead3cc81ceb9c46002127ba222dfee

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In Geometry and Topology

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Citations in the corpus

Bifurcations of piecewise smooth flows: Perspectives, methodologies and open problems (2012, methodology): “An extension to sliding bifurcations was presented in [66], where maps are derived that correct for the presence of the discontinuity when applied to a smooth flow continued from one side of the switching boundary.”
Bifurcations in Nonsmooth Dynamical Systems (2008, background): “The proof of the above theorem can be found in [44].”
The nature of the normal form map for soft impacting systems (2008, background): “[22,23] analysed various types of non-smooth mechanical systems allowing grazing condition.”
Generic bifurcations of low codimension of planar Filippov Systems (2011, background): “10 and they are usually called switching-sliding bifurcation [6,7] or buckling bifurcation [17].”
A Filippov sliding vector field on an attracting co-dimension 2 discontinuity surface, and a limited loss-of-attractivity analysis☆ (2013, background): “[4,5,13,22]; for works on the class of complementarity systems, see [14], for works from the point of view of bifurcations of dynamical-systems see [7,16,15,19]; and, of course, see the classical references [3,11,26,27] for a thorough theoretical introduction to these systems.”
Two-parameter degenerate sliding bifurcations in Filippov systems (2005, unknown): “Systems with discontinuous vector fields (or Filippov systems) were recently shown to exhibit a novel class of Cbifurcations termed as sliding bifurcations[9].”
Numerical sliding bifurcation analysis: an application to a relay control system (2003, background): “However, sliding bifurcations of limit cycles in -dimensional systems have been recently classified [4].”