Examinando por Materia "bifurcation theory"

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    Analyzing sliding bifurcations on discontinuity boundary of Filippov systems
    (WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC, 2008-01-01) Arango, Ivan; Taborda, John Alexander; Arango, Ivan; Taborda, John Alexander; Universidad EAFIT. Departamento de Ingeniería Mecánica; Mecatrónica y Diseño de Máquinas
    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.