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https://hdl.handle.net/10784/29331

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Examinando Documentos de conferencia por Materia "Bifurcation theory"

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    Detecting Sliding Areas in Three-Dimensional Filippov Systems using an Integration-Free Method
    (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 detect sliding areas in three-dimensional (3D) Filippov systems using an integration-free method denominated Singular Point Tracking (SPT). Many physical applications in engineering can be modelled as Filippov systems. Sliding dynamics due to nonsmooth phenomena as friction, hysteresis or switching are inherent to Filippov systems. The analysis of sliding dynamics has many mathematical and numerical difficulties. Several well-known numerical problems can be avoid using integration-free methods. In this paper, we extend the SPT method to 3D Filippov systems. In comparison with the 2D case, the evaluation of the vector fields on the discontinuity boundary (DB) should be reformulated and new dynamics on DB should be characterized.
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    SPTCont 1.0: A LabView Toolbox for Bifurcation Analysis 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 report the development of LabView toolbox for bifurcation analysis of Filippov systems, which we are denominated SPTCont 1.0. This toolbox is included in the GAONDYSY software developed in language G for analysis of non-smooth dynamical systems. The SPTCont 1.0 uses integration-free algorithms based on the evaluation of the vector fields on the discontinuity boundary (DB). The routines apply the classification of points and events on DB recently proposed. Local and global bifurcations can be detected using the numerical method Singular Point Tracking or SPT. The lines and the points on DB are characterized with didactic symbols and the exclusive conditions for their existence based on geometric criterions. Boolean-valued functions are used to formulate the existence conditions. Two-dimensional and three-dimensional problems can be studied with the software SPTCont 1.0. Two principal advantages have the software in the analysis of nonsmooth systems. First, the software has educational and didactic subroutines for amateur users. Second, the software has functions for specialyzed. users where the integration-free algorithms in the SPT avoid the well know numerical problems of these algorithms. If the integration is unavoidable, for example in detection of global bifurcations, the SPT method computes the initial condition of the simulation to reduce the compute time.