SPTCont 1.0: A LabView Toolbox for Bifurcation Analysis of Filippov Systems
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2008-01-01
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WORLD SCIENTIFIC AND ENGINEERING ACAD AND SOC
Resumen
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.