Publicación: Analyzing sliding bifurcations on discontinuity boundary of Filippov systems
Fecha
2008-01-01
Autores
Arango, Ivan
Taborda, John Alexander
Título de la revista
ISSN de la revista
Título del volumen
Editor
WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC
Resumen
In this paper, we propose a novel method to analyze sliding bifurcations in discontinuous piecewise smooth autonomous systems (denominated Filippov systems) on the planar neighborhood of the discontinuity boundary (DB). We use a classification recently proposed of points and events on DB to characterize the one-parameter sliding bifurcations. For each parameter value, crossing and sliding segments on DB are determined by means of existence conditions of two crossing points (C), four non-singular sliding points (S) and thirty-five singular sliding points (T, V, Pi, Psi, Q or Phi). Boolean-valued functions are used to formulate these conditions based on geometric criterions. This method was proven with the full catalog of local bifurcations that it was proposed recently. A topological normal form is used as illustrative example of the method.