Characterizing Points on Discontinuity Boundary of Filippov Systems

I. Arango and J.A. Taborda (Colombia)


Modelling, simulation, numerical methods, nonsmooth systems and bifurcation theory.


In this paper, we presented a basic methodology to under stand the behavior of discontinuous piecewise smooth au tonomous systems (denominated Filippov systems) in the planar neighborhood of the discontinuity boundary (DB). This methodology is useful in detection of nonsmooth bi furcations in Filippov systems. We propose a classifica tion of the points and events on DB. This classification is more complete in comparison with the reported papers pre viously. The lines and the points are characterized with di dactic symbols and the exclusive conditions for their exis tence based in geometric criterions. Boolean-valued func tions are used to formulate the conditions. An illustrative example with a friction oscillator is presented.

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